# Differential equation- Math

151,510 results

**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.

**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.

**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 ...

**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)=

**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!

**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

**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), ...

**Ordinary Differential Equation**

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

**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?

**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.

**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.

**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.

**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) ...

**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 ...

**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?

**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.

**DIFFERENTIAL EQUATION**

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

**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...

**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 ...

**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, ...

**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 ...

**maths(Differential Equation)**

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

**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:

**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 ...

**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.

**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.

**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

**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

**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.

**differential equations**

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

**Differential Equations**

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

**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...

**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...

**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...

**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.

**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?

**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.

**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

**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...

**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 ...

**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

**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.

**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 ...

**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...

**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 ...

**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 ...

**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

**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...

**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.

**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...

**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 ...

**Math**

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

**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.

**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?

**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= ______

**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)

**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

**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

**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...

**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...

**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 ...

**math**

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

**Math**

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

**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 ...

**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...

**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...

**Math DE**

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

**Math, Differential Equation**

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

**Calculus**

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

**math**

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

**math**

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

**math**

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

**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^...

**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...

**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 ...

**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)=___________________

**Math**

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

**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)

**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).

**math**

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

**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...

**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

**differential equation**

i need help understanding this question? can some one tell me what exactly i have to do in it 7. Suppose a student carrying a flu virus returns to an isolated college campus of 1000 students. Determine a differential equation for the number of people x(t) who have contracted ...

**Differential Equation**

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

**Calculus**

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

**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.

**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 ...

**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 ...

**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!

**Engineering Math**

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

**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.

**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...

**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 ...

**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

**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!!

**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.

**Differential Equation**

Verify whether the given equation (y=x^2+4x) is a solution to this given equation [(xdy/dx)=x^2+y]

**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 ...

**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...

**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)