Number of results: 150,864

**ordinary differential equation**

consider the differential equation d^3x/dt^3 - 9(d^2x/dt^2)+ 27(dx/dt) -27x = c0s t +sin t + te^(3t) a) show that characteristic equation of the differential equation is (m-3)^3 =0 (b) Hence, find the general solution of the equation.

*May 21, 2016 by thigan*

**Math**

The maximum number of arbitrary constants is equal to a. Number of derivatives in the differential equation b. Degree of differential equation c. Order of differential equation e. None of the above I don't understand this, but my guess it's letter A. Please help.

*September 13, 2014 by Rin*

**calculus-differential equation**

Consider the differential equation: (du/dt)=-u^2(t^3-t) a) Find the general solution to the above differential equation. (Write the answer in a form such that its numerator is 1 and its integration constant is C). u=? b) Find the particular solution of the above differential ...

*February 5, 2008 by Jeff*

**Differential Equations**

in this problem we consider an equation in differential form M dx+N dy=0 (2y-2xy^2)dx+(2x-2x^2y)dy=0 give implicit general solutions to the differential equation. F(x,y)=

*February 15, 2016 by Anonymous*

**Calculus**

Solve the differential equation dy/dx = -xe^y and determine the equation of the curve through P(1,2) I tried solving the differential equation and I get y = log(x^2/2 + C). Is this correct? Now I forgot how to find the equation. Thank you!

*August 6, 2012 by Robert*

**math (differential equation)**

show that y sub n=cos(ncos^-1(x)) satisfies the differential equation: (1-x^2)(d^2y/dx^2)-x(dy/dx)+n^2(dy/dx)=0

*March 3, 2013 by shoosh*

**PLEEEEEAAAASE HELP WITH DIFFERENTIAL EQ PROBLEMS!!**

1) What are the equilibrium solutions to the differential equation and determine if it is stable or unstable with the initial condition y(-4)=1: 0.1(y+2)(4-y) 2) Use Euler's method with step size=0.5 and initial condition y(0)=3 to solve the equation y(0)=3 to estimate y(2), ...

*December 8, 2014 by Karen*

**Ordinary Differential Equation**

Form the differential equation of the family of straight line with slope and y- intercept equal

*February 19, 2017 by Bilal*

**Calculus**

Consider the differential equation dy/dx = x^4(y - 2). Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 0. Is this y=e^(x^5/5)+4?

*March 3, 2017 by Anonymous*

**Calculus**

Consider the differential equation dy/dx = x^2(y - 1). Find the particular solution to this differential equation with initial condition f(0) = 3. I got y = e^(x^3/3) + 2.

*March 6, 2017 by Anonymous*

**calculus differential equation**

Find in implicit form the general solution of differential equation dy/dx=2(e^x-e^-x)/y^2(e^x+e^-x)^4 with (y>0). I know this requires a seperation of variables but I beyond that I am confused by how.Thanks.

*February 12, 2011 by malcolm*

**calculus differential equation**

Find in implicit form the general solution of differential equation dy/dx=2(e^x-e^-x)/y^2(e^x+e^-x)^4 with (y>0). I know this requires a seperation of variables but I beyond that I am confused by how.Thanks.

*February 12, 2011 by malcolm*

**Calculus**

Which of the following is a separable, first-order differential equation? A) dy/dx= x+y/2x B) dy/dx=x+y/x-y C) dy/dx=sinx << D) dy/dx=xy/x+y E) dy/dx= 2lnxy 2) The differential equation dy/dx=y/x^2 has a solution given by: A) y=C sqrt(x^2+4) B)y=C e^-1/x C)-1/2ex^2+C D) ...

*May 8, 2014 by Samantha*

**Help with differential eqs problem???? (Calculus)**

Consider the differential equation dy/dt=y-t a) Determine whether the following functions are solutions to the given differential equation. y(t) = t + 1 + 2e^t y(t) = t + 1 y(t) = t + 2 b) When you weigh bananas in a scale at the grocery store, the height h of the bananas is ...

*November 30, 2014 by Stacey*

**Differential equation (urgent pls!!!)**

Reduce the differential equation below to an exact equation (X - 2siny + 3)dx -(4siny - 2x + 3)dy=0. The problem here is how to solve for the integrating factor...any help pls?

*March 4, 2016 by BEN*

**Calculus**

Consider the differential equation dy/dx=xy-y. Find d^2y/dx^2 in terms of x and y. Describe the region in the xy plane in which all solutions curves to the differential equation are concave down.

*May 1, 2014 by Michelle*

**DIFFERENTIAL EQUATION**

find the differential equation of family of lines with slope and y intercept equal.

*June 16, 2012 by JAJA111111*

**math**

a bank account earns 7% annual interest compounded continuously. you deposit $10,000 in the account, and withdraw money continuously from the account at a rate of $1000 per year. a. write the differential equation for the balance, B, in the account after t years b. what is the...

*March 14, 2011 by Anonymous*

**Math**

For the harmonic potential V(x,y) = x^2 + y^2 a) Find the total differential, dV. For this I got dV = 2x.dx + 2y.dy b) Given that -dV = F(x).dx + F(y).dy, where F(x) and F(y) is the force in the x and y direction, respectively, write a differential equation describing the ...

*November 18, 2008 by Beth*

**math**

The displacement s (in metres) of a body in a damped mechanical system, with no external forces satisfies the following differential equation: 6 3 2 2 dt ds dt d s where t represents time in seconds. If at time t = 0, s = 0 and 5 dt ds m/s, ...

*May 17, 2011 by Karl Haxell*

**Differential Equations**

The velocity v of a freefalling skydiver is well modeled by the differential equation m*dv/dt=mg-kv^2 where m is the mass of the skydiver, g is the gravitational constant, and k is the drag coefficient determined by the position of the driver during the dive. (a)Find the ...

*January 24, 2013 by Erica*

**maths(Differential Equation)**

Solve the differential equation below (Y + y^3/3 + x^2/2)dx + 1/4(1 + y^2)xdy=0

*March 3, 2016 by BEN*

**math numerical methods**

Consider the following second order differential equation: y"-2x^(2)y+y^(3)=17cos(4x) with y(0)=4 , y'(0)=-9 If we let u=y and v=y′ then as an AUTONOMOUS first order system, the second order differential equation is correctly expressed as:

*April 21, 2013 by mahdi*

**Math**

a weight of mass m is attached to a spring and oscillates with simple harmonic motion. By Hooke's Law, the vertical displacement, y(t) satisfies the differential equation dy/dt=sqrt(k/m)*sqrt(A^2-y^2) where A(Fixed) is the maximum displacement and k is a constant, solve this ...

*December 15, 2012 by A.J.*

**Physics**

Verify that the formula u(t)=Acos(ωo*t+Φ) is a solution to the differential equation for the mass on a spring, by plugging this expression for u(t) directly into the differential equation: d^2u/dt^2+ωo^2*u=0.

*March 10, 2016 by Anonymous*

**math**

10. Sales of televisions grow at a rate proportional to the amount present (t is measured in days). (a)Set up a differential equation to model this problem. (b)Solve the differential equation if at t = 0, there are 20 televisions sold and after 3 days, 500televisions are sold.

*May 31, 2007 by dougal*

**calculus**

verify that y=c/x^2 is a general solution of the differential equation y'+(2/x) y=0-6y=0 then find a particular solution of the differential equation that satisfies the side condition y(1)=2

*April 10, 2012 by mari*

**differential equation**

A simple pendulum of length l, is oscillating through a small angle theta, in a medium for which the resistance is proportional to the velocity. Obtain the differential equation of its motion and discuss the motion

*March 10, 2011 by aamiraa*

**differential equation**

A simple pendulum of length is oscillating through a small angle θ in a medium for which the resistance is proportional to the velocity. Obtain the differential equation of its motion and discuss the motion.

*March 14, 2011 by shasha*

**differential equations**

solve the differential equation by seperation of variables 5. y'=xy/2ln y

*March 17, 2011 by cathy*

**Differential Equations**

Solve the seperable differential equation for U. du/dt = e^(5u+7t) - Using the following initial condition U(0) = 12

*August 27, 2011 by Kody*

**Differential Equations**

Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when t<=0, but that are nonzero when t>0...

*January 31, 2013 by Erica*

**Differential Equations**

Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when t<=0, but that are nonzero when t>0...

*January 31, 2013 by Erica*

**Calculus!!**

Consider the differential equation given by dy/dx = xy/2. A. Let y=f(x) be the particular solution to the given differential equation with the initial condition. Based on the slope field, how does the value of f(0.2) compare to f(0)? Justify your answer. B. Find the particular...

*April 23, 2016 by Anonymous*

**Differential equations**

((3y^2)dx/(x^2+3x)) +( ( 2y ln ((5x)/(x+3))+ 3siny)dy=0 Please help me in solving this problem using exact differential equation. Thanks in advance.

*September 21, 2016 by Anonymous*

**AB Calculus**

So I'm supposed to verify the solution of the differential equation. The solution is y=e^(-x). The differential equation is 3y' + 4y = e^(-x). What is the problem asking me to do here?

*February 27, 2012 by Hannah*

**Calculus - Differential Equations**

Use separation of variables to find the solution to the differential equation: 4 (du/dt) = u^2, subject to the initial condition u(0)=6.

*November 4, 2016 by James*

**Differential Equations**

Solve the differential equation below with initial conditions. Compute the first 6 coefficient. Find the general pattern. (1-x)y"-y'+xy=0 y(0)=1, y'(0)=1

*July 9, 2012 by Jason*

**Differential Equations**

Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when t<=0, but that are nonzero when t>0...

*January 31, 2013 by Erica*

**Chemistry/Math**

Write a differential equation describing a second order reaction – a reaction in which the rate of depletion of the concentration of the reactants depends on the square of reactants’ concentration. Solve this differential equation and hence find an expression for the ...

*November 10, 2008 by Alice*

**Differential Equation**

Hello everyone. I was wondering if anyone knows a site that could help me with the homework free online...with Differential equations. it would be great. I need help on in big time thank you

*October 22, 2008 by mary*

**calculus**

is y = x^3 a solution to the differential equation xy'-3y=0?? how do i go about solving this??? also, is there a trick to understanding differential equations? i'm really struggling with this idea, but i'm too embarassed to ask my professor for help.

*December 1, 2008 by Kenneth*

**differential equations**

Consider the 2nd order differential equation: x''(t)=-x-A(x^2-1)x'(t) x(0)= 0.5 x'0)= 0 ''= 2nd order,'= 1st order where A is a positive constant.As the value of A increases this equation becomes increasingly stiff. Convert this equation to two first-order equations. please ...

*November 16, 2011 by Rikki*

**Calculus - Differential Equations**

Use separation of variables to find the solution to the differential equation: 4 (du/dt) = u^2, subject to the initial condition u(0)=6. So far, I have: 4 du = u^2 dt 4/u^2 du = dt -4/u = t+C I am unsure what to do from this point...

*November 4, 2016 by Abby*

**Differential Equation 4**

A differential equation governing the velocity v of a falling mass m to air resistance proportional to the square of the instantaneous velocity is m dv/dt=mg-kv^2 where k>0 is a constant of proportionality. The positive direction is downward. (a)Solve the equation subject ...

*April 6, 2015 by ijat*

**Math**

I need to solve this set of differential equations {y'+(t/2)1, y(0)=1} and then find the limiting value as t approaches infinity. I'm not sure where to start. I found the answer to the differential equation to be: y(t)=e^-t^2/4[e^(r^2/4)dr +Ce^(-t^2/4)where the [ sign ...

*September 6, 2012 by Emily*

**calculus**

consider the differential equation dy/dx= (y - 1)/ x squared where x not = 0 a) find the particular solution y= f(x) to the differential equation with the initial condition f(2)=0 (b)for the particular solution y = F(x) described in part (a) find lim F(x) X goes to infinity

*May 19, 2008 by sammy*

**calculus**

determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false a) the function f(x)=3/2 +cx^-2 is a solution of the differential equation xy'+2y=3 b) the differential equation dy/dx= (f(x)g(y...

*April 10, 2012 by jhony*

**Differential Equations**

Find the general solution of the differential equation specified. 1) dy/dt= 1/(ty+1+y+1) 2) dy/dx=sec y I got y(x)=arcsin(x) for the second one. I'm not sure what to do with the first one.

*January 22, 2013 by Erica*

**Differential equation **

A spherical balloon remains spherical as it is slowly inflated. The radius of the balloon r (in cm) at time t (in seconds) satisfies the differential equation. Dr/dt = k/r^2 where k is a positive constant. When the radius is 3 cm, the radius is increasing at the rate of 5/36pi...

*February 19, 2017 by Anon*

**Physics**

For the harmonic potential V(x,y) = x^2 + y^2 a)Find the total differential, dV. b) Show that dV is exact c) Given that -dV = Fx.dx + Fy.dy where Fx and Fy is the force in the x and y direction, respectively, write a differential equation describing the change of potential ...

*November 14, 2008 by Beth*

**Math**

Fnd the equation of the curve through the point (-1,2) of the differential equation dy/dx = -2xy/(x^2+1)

*February 11, 2016 by Ri*

**Differential equation- Math**

Find the general solution of the following system of equation? Please help, i don't know what to do... dx/dt = 3x +2y +2z dy/dt = -5x - 4y - 2z dz/dt = 5x + 5y +3z.

*March 17, 2011 by katie*

**differential equation!!**

How can I solve the differential equation? C = 15ð(2Dh+(3/4)D²) + ë (94.25 Dh+35.34 D^2)/(pi D^2h/4) first dC/dD? second d^2C/dD^2? first dC/dh? second d^2C/dh^2?

*November 23, 2010 by Alicia*

**math**

Can someone please help? Solve the differential equation dy/dx = 6xy with the condition y(0) = 40 Find the solution to the equation y= ______

*May 19, 2013 by mark*

**calculus**

Can you give me a good website on the topic, slope fields and differential equations? I need to match six slope fields with the correct differential equation. 1. dy/dx=x-y 2. dy/dx=1+x 3. dy/dx=cosx 4. dy/dx=2x 5. dy/dx=x+y 6. dy/dx=y(2-y)

*November 7, 2007 by Anonymous*

**ordinary differential equation**

Solve the simultaneous differential equations L(di1/dt)+Ri1+(1/2)L(di2/dt)=E L(di2/dt)+Ri2+(1/2)L(di1/dt)=0 where 𝐿, 𝑅, and 𝐸 are constants and given that i1=i2=0 when t=o

*May 21, 2016 by thigan*

**Math**

An explicit solution of a differential equation is: a) a simpler equation b) a real number c) a function on some domain d) an approximation e) a linear relation

*February 2, 2016 by Rose*

**Ap Calculus**

Ok, I've been doing BC review tests to prepare for the AP exam. I came across this free response problem and I have no idea how to do it, can someone please help me with this? It gives the differential equations: dP/dt = .03P(30-P) and it asks "Find the general solution to the...

*April 25, 2007 by Jessica*

**Differential equations in Calculus...plsssss help?**

Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T + 5. a) Supposes that T(0) = 105. What does the...

*November 30, 2014 by Bridget*

**Chemical Engineering**

When a manometer is subjected to a time dependent pressure differential, the level of liquid in the legs changes with time according to the equation: (L/g)*(d^2h/dt^2)+(8uL/ygr^2)*(dh/dt)+h = dp/yg where L = length of liquid in tube, h is the height differential, dp is the ...

*May 12, 2015 by Brandy*

**math**

how do you find the differential equation for t(dy/dt)+9y=8t and y(1)=6?

*January 29, 2009 by alice*

**Math**

What will be its differential equation? y^2-2xy+x^2=a^2

*February 11, 2016 by Ri*

**MATH**

Differential equations, initial value problem. The general equation of motion is: mx"+Bx'+kx=f(t), where the independent variable is t, and the displacement x is the dependent variable. In this case, external force f(t)=0, so mx"+Bx'+kx=0 substitute m=0.25, k=4, B=1 we have a ...

*March 16, 2011 by Anonymous*

**Differential Equations**

(a) Let S be the set of solutions y(t) to the differential equation dy/dt = -y for t> 0. With addition and scalar multiplication of elements defined in the usual way, is S a vector space? (b)Let T be the set of solution y(t) to the differential equation dy/dt = 1 - y for t...

*October 13, 2014 by Cam*

**I would like to understand my calc homework:/**

Consider the differential equation given by dy/dx=(xy)/(2) A) sketch a slope field (I already did this) B) let f be the function that satisfies the given fifferential equation for the tangent line to the curve y=f(x) through the point (1,1). Then use your tangent line equation...

*March 27, 2013 by Amber*

**Math DE**

Find the general solution of the differential equation dy/dx-4y= -5y^2

*August 3, 2014 by Cam*

**Math, Differential Equation**

3ydx= (3(x^2) -1)(dx-dy). Solve by Linear. Thanks!

*September 28, 2015 by Jhun*

**Calculus**

Find the particular solution of the differential equation particular solution of the differential equation dy/dx=(x−7)e^(−2y).

*November 15, 2013 by Robin*

**math**

f"(x)=2, f'(2)=5, f(2)=10. solve this differential equation by finding the particular solution. How do you do this?

*December 1, 2009 by Ed*

**math**

can someone elxplai to me how to solve this differential equation. dy/dx= (x^2+3y^2)/2xy

*June 18, 2015 by Anonymous*

**math**

For what values of r does the function y = erx satisfy the differential equation y'' − 6y' + 3y = 0?

*January 12, 2017 by Sara*

**Basic Differential Equation**

Hi all. I need help understanding something my book dosn't go over well. For example dy/dx=-4y is a given solution and I need to find the differential equation. I simply isolate y then integrate. Getting y=e^(-4x) which is correct. My question is for something like (d^2y)/(dx^...

*June 5, 2015 by Joe*

**calculus**

Sorry to post this again, but I am still unable to understand it and need help. Please help.1) Using 3(x-3)(x^2-6x+23)^2 as the answer to differentiating f(x)=(x^2-6x+23)^3/2, which I have been able to do, I need to find the general solution of the differential equation dy/dx...

*May 22, 2011 by Claire*

**Differential Equations**

a) Sketch the phase line for the differential equation dy/dt=1/((y-2)(y+1)) and discuss the behavior of the solution with initial condition y(0)=1/2 b) Apply analytic techniques to the initial-value problem dy/dt=1/((y-2)(y+1))), y(0)=1/2 and compare your results with your ...

*February 3, 2013 by Erica*

**Math**

Find the general solution F(x,y)=C of the differential equation: (-3(x^2)y-8x)dy+(-3xy^2-8y)dx=0 Where F(x,y)=___________________

*January 22, 2013 by Bob*

**Math**

Determine the solution to the initial value differential equation: y′+2*y^2*e^(5*x)= 0 y(0)=2

*October 21, 2009 by AK*

**math**

find general solution in implicit form of differential equation dy/dx= 2(e^x-e^-x)/y^2(e^x+e^-x)^4 (y>0)

*February 11, 2011 by mike*

**math**

The function y_p(t) =ln(4 + 2 t), t > -4/2, is a particular solution to the differential equation y''+8y=g(t). Find g(t).

*October 13, 2014 by diego*

**math**

find the linear differential equation that has y=5-x+2e^xsin3x as a particular solution

*July 21, 2015 by toby*

**Calculus**

dy/dx = 4ye^(5x) a) Separate the differential equation, then integrate both sides. b) Write the general solution as a function y(x). For the second part, I got y(x)=e^((5e^(5x))/(5)) + C but I don't understand how to separate differential equations and/or integrate both sides...

*June 16, 2014 by Jamie*

**Differential Equations**

A rabbit starts at the origin and runs up the right branch of the parabola y=x^2 with speed a. At the same time a dog, running with speed b, starts at the point (c,0) and pursues the rabbit. Write a differential equation for the path of the dog

*January 26, 2012 by Samantha*

**Differential Equation**

Find the general solution of (D^2-3D+2)(D-5)^Dy=0. (Hint:Use the auxiliary equation)

*July 14, 2012 by Maegan*

**Calculus**

solve the differential equation dy / dx = 11x^2y^2 with the condition that y(0) = 4 The solution to the equation is y =

*November 26, 2014 by Anonymous*

**CACULUS**

dy/dx = (y-1)^2 cosπx There's a horizontal line with equation y=c that satisfies this differential equation. Find the value of c.

*February 11, 2009 by JIM*

**Differential Equations**

a) Sketch the phase line for the differential equation dy/dt=1/((y-2)(y+1)) and discuss the behavior of the solution with initial condition y(0)=1/2 b) Apply analytic techniques to the initial-value problem dy/dt=1/((y-2)(y+1))), y(0)=1/2 and compare your results with your ...

*February 3, 2013 by Erica*

**Differential eqns**

a) Sketch the phase line for the differential equation dy/dt=1/((y-2)(y+1)) and discuss the behavior of the solution with initial condition y(0)=1/2 b) Apply analytic techniques to the initial-value problem dy/dt=1/((y-2)(y+1))), y(0)=1/2 and compare your results with your ...

*February 3, 2013 by Erica*

**Calc**

I have the differential equation dP/dt = 0.5(800-P) and I need to get the population equation P(t). Can someone walk me through the steps? Thanks!

*May 6, 2012 by Kris*

**Engineering Math**

solve the 1st differential equation: y1+4y=cos(x) with intial condition y(pie/3)=1

*June 24, 2011 by Thomas*

**calculus**

d=dmax (1-e^(-kt)) This equation is the result of integrating an ordinary differential equation. Derive that ODE and the associated initial condition.

*March 7, 2009 by dolphin1384*

**Differential equations,Calculus**

So I have the following differential equation. The general solution I have is: t=k(-1/r)+c I now need to find the particular solution when t=0 and the radius (r) = 1cm. So k is a constant which is approx 3.9 (5/4pi) So for the particular solution im really just plugging in the...

*February 22, 2017 by Anon*

**Calculus**

I'm having trouble with part of a question in a problem set. The question reads as follows: Continuous price discounting. To encourage buyers to place 100-unit orders, your firm's sales department applies a continuous discount that makes the unit price a function p(x) of the ...

*October 16, 2009 by Kelly*

**Math**

Hi. please help me solve the ffg. differential equation: D^2y=3sinx-4y given y=0 and dy/dx=1 at x=pie/2 Need full solution. Tx

*February 27, 2013 by Ash*

**Math**

Form the differential equation of the family of curves y^2-2xy+x^2=a^2, a=arbitary const. I really need to know the answer!!

*February 11, 2016 by Ri*

**Math**

Find the general solution to the differential equation that models the statement:"The rate of change of P with respect to x is proportional to 15-x.

*February 17, 2016 by Dea*

**differential equation**

in the theory of learning the rate at which the subject is memorized is assumed to be directly proportional to the amount left to be memorized. also the rate at which the subject is forgotten is directly proportional to the amount memorized in their time t. suppose M denotes ...

*October 26, 2014 by Anne*

**Differentail Equations**

I cant figure out how to do this type of problem! Consider the first order differential equation y′+(x/(x^2−4))y=(e^x)/(x−9) For each of the initial conditions below, determine the largest interval a<x<b on which the existence and uniqueness theorem for...

*June 6, 2015 by Eric*

**math**

how do i solve differential equation dy/dx=3/(2-x) and use graphing utility to graph 3 solutions,one which passes through the point(1,0)

*January 21, 2011 by mrunal*

**Calculus**

The rate of decay is proportional to the mass for radioactive material. For a certain radioactive isotope, this rate of decay is given by the differential equation dm/dt = -.022m, where m is the mass of the isotope in mg and t is the time in years. A. If m(0)=20, write a ...

*April 23, 2016 by Anonymous*

**differential equation**

xy

*June 19, 2012 by sd*