# math- differential equations

138,750 results

### Differential Equations

Classify the following differential equations as linear or nonlinear: 3x' +5x=7t^2 4x^2+2x+5tx=0

### Differential Equations!

I'm struggling solving this separable differential equations: (du/dv) = ((uv+u)/(uv+v)) I multiplied both sides by dv to get on the left side just du and cancel out dv, but after that don't know where to go. I've tried integration by parts but it doesn't look right! Any help ...

### 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)=

### Math

A two population model is satisfied by a system of differential equations given by, V(x,y) = (ax,by)^T The general solution of the system of differential equations has x = áe^at for some constant á. The parameter t can be eliminated and we can express y in terms of x in the ...

### 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

((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.

### 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 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.

### 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...

### 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...

### 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 ...

### 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 ...

### 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 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 ...

### PLEASE HELP WITH DIFFERENTIAL EQUATIONS QUESTION??

Which of these equations have an equilibrium solution. What are they? How are their DE's different? dy/dx=6y-y^2 dy/dx 15-3y

### 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

### 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

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...

### 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...

### math

Solve the following ordinary differential equations. I) (2y+x^2+1)dy/dx+2xy-9x^2=0 ii) d^2/dx^2+3day/DX+2y=x^2

### math-differential equations

hi i need to know how to do this one thanks Find the solution to yx + x + (dy/dx) = 0 ; y(9) = -9 y = ???? Does this separate the variables? dy/dx=-x(y+1) dy/(y+1) = -x dx

### University, Engineering Math

solve the ffg. differential equations: 1. x^3 +(y+1)^2 dy/dx=0 2. dy/dx-(1+1/x)y=y^2 3. dy/dx + ytanx=y^3sec^4x

### differential equations

Convert x''+ sin(x) = 0 into a first order system of equations. (x'' refers to the second derivative of x). I tried: y1 = sin(x) y2 = x' {y1' = cosx {y2' = -sinx Not sure if I did it right.

### Differential Equations

Consider the system shown below of two masses of mass m, coupled together between two fixed walls via springs with varying spring constants. Let x(t) and y(t) be the horizontal displacements of the two masses as a function of time. (a)Write down a system of differential ...

### Math

Are the differential equations separable or not? 1. y'= ye^(x+y) 2. y'= ye^(xy) 3. y'= y(xcos(y)) If they are, could you show how? Any help, even on one, would be extremely appreciated!

### 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

### 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.

### 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...

### math- differential equations

This is what im given (1 + x)dy/dx - xy = x + x2 ____________________________________________________________________________________________________________________________________________________________ From my understanding I should move everything to one side like: (1 + x...

### Differential Equations

(x^2+1)dx+x^2y^2dy=0 need help:)..thanks.

### Differential Equations

(D^2 + 1) y = sec^2 2x solve for Yp.

### Differential Equations

(D^2 + 1) y = sec^3 x solve for Yp.

### Differential Equations

(D^2 + 1) y = 1/(1 + sin x) solve for Yp.

### Differential Equations

Solve x(dy/dx)=(y^2)/(1-y log x).

### Differential Equations

(D^2 + 1) y = sec^2 (x) tan (x) solve for Yp.

### differential equations

rk4 method with h 0.1 solve for y' = 4x-2y, y(0)= 2; y(0.5)

### 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 ...

### Calculus

Are the following differential equations separable or not? * y'= ye^(x+y) * y'= ye^(xy) * y'= y(xcos(y)) I am no good at these :[

### Calculus AB

Verify if the given equations are solutions to the differential equation. dy/dt=k(y-a) i) y=1-ae^(kt) ii) y=a+Ce^(kt)

### Differential Equations

Find the eigenvalues and eigenfunction for the BVP: y ' ' '+ λ2 y ' = 0 , y(0) = 0, y’(0) = 0 and y’(L) = 0

### maths-urgently needed[Differential equations]

solve- dy/dx = 2xy + (y^2/x^2)

### maths-urgently needed[Differential equations]

solve- dy/dx = 2xy + (y^2/x^2)

### differential equations

the general solution of the diff. eq. y' = (1/x)(y/(1-y)) - (1-x)(y/(1-y)) in implicit form is?

### Math: Differential Equations

I've been stuck on this math hw problem for a while, I was thinking of taking the integral of the equation, but I've been messing up too much that I'm not sure anymore. Q: Is it possible to solve y'=x/(x^(2)-1) for y(1) = 0? Thank you!

### calculus

solve the differential equations subject to the given conditions. dy/dx= 4x^1/2 y=21 of x=4 is this derivative?!

### Differential Equations

y'=2x+y. Find a solution whose graph is also an isocline.

### 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...

### Differential Equations (Another) Cont.

For the following initial value problem: dy/dt=1/((y+1)(t-2)) a)Find a formula for the solution. b) State the domain of definition of the solution. c) Describe what happens to the solution as it approaches the limit of its domain of definition. Why can't the solution be ...

### 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.

### differential equations

dy/dx=4x/y..verify that the straight lines y=2x are solution curves, provided x doesnt equal 0.

### mathematics

Solve the following differential equations: (I). Cos x dy/dx + ysin x= sec^2 x (II). Y"-10y' + 41y=0

### 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...

### math

Can someone please explain this problem Find the general solution to the linear system of differential equations. x'1 x'2 x'3 = −4 −4 5 0 −4 4 0 4 2 x1 x2 x3

### 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

### Calculus - Second Order Differential Equations

Posted by COFFEE on Monday, July 9, 2007 at 9:10pm. download mp3 free instrumental remix Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2...

### 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 Equations

Use the Laplace Transform to solve this initial value problem. y'''' - 8y = 0, y'(0)=63, y''(0)=216, y'''(0)=297 I would really appreciate the help.

### Math: Differential Equations

I'm given y''= sin(x) with the initial conditions of y(0)=0 and y'(0)=2. I've already taken the integral two times to get an answer of y= -sin(x)+3x, however, I'm stuck as to how to make this equation in terms of x=... Please explain, I'd really appreciate it!

### Math, Calculus

help Please... Differential Equations Problems... please give the complete solution, so that i can understand how it is derived... tnx in advance, god Bless... Here are the problems : 1.) y dx + (2x+3y)dy = 0 2.) (2xy + y^(2) ) dx - 2x^(2) dy = 0 ;y = e, x = e 3.) y( x^(2) + ...

### 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 Equations

Verify whether the given equation(y=c1-cos(x+c2)) is a solution to this equation[(d^2y/dx^2)^2 + (dy/dx)^2 - 1 = 0].

### Calculus

Integrate e^(-x^2/2) dx What branch of calculus is this? Is this differential equations?

### Calculus Please help!

The differential of the function y=(x^2+6)^3 is dy=______dx. When x=2 and dx=0.05, the differential dy=_______? A) dy=______dx? B) the differential dy=_______?

### Math

Find the specific solution for the following differential equations: a) (dy/dx)^2 - x^4 = 0 given the initial value y(1) = 0 b) dy/dx = ysinx given the initial value y(pi) = 1

### MATH

Solve the differential equations? (calculus) a) square root cotany/ (1+x^2)sin^5y dy/dx = e^x^3 +3x/ square root cotany b) y^2/cosx dy = e^sinx/ e^y^3-1 dx

### 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 ...

### 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), ...

### Math

help Please... Differential Equations Problems... please give the complete solution, so that i can understand how it is derived... tnx in advance, god Bless... Here are the problems : 1.) y dx + (2x+3y)dy = 0 2.) (2xy + y^(2) ) dx - 2x^(2) dy = 0 ;y = e, x = e 3.) y( x^(2) + ...

### Calculus

Find the particular solution of differential equations that satisfies the initial condition dx/dy=e^(x+y) x(1)=0 I know you have to get all the y and dy on one side and x and dx on the other so you can intagrate and stuff, but im having trouble getting there

### college differential equations

Find two linearly independent power series solutions to the diffrential equation. State the first 3 therms of each series: 2x^2y''+xy'-(1+2x^2)y=0

### Differential Equations

Solve dy/dx = y/(2y-x) using rational substitution (using v=y/x) with the initial condition y(0)=1. I solved this problem and found C (the constant) to be undefined. That is not the correct answer.

### Math: Differential Equations

Solve the initial value problem y' = y^2, y(0) = 1 and determine the interval where the solution exists. I understand how the final solution comes to y = 1/(1-x), but do not understand how the solution is defined from (-infinity, 1) and not (1, infinity).

### Calc 2 college

Modeling with differential equations. If a bacteria culture doubles every 10 minutes and the original culture has 300 cells determine the rate of growth.

### 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...

### Differenctial equations

Use the change of variable x = exp(s) to recast the differential equation xy′′+y′+(L/x)y=0 Please HELP ME

### 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

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 ...

### Math 116

Consider the following system of equations. y=2x-2 y-2x=9 What can you conclude about the system of equations? a. The system of equations is inconsistent. b. The system of equations is dependent. c. The system of equations is independent. d. none of these.

### college math/chemistry

chemical reaction: E + S <=> E~S <=> E-S <=> indicates a bidirectional reaction with different forward and backward rate constants. we can call these k1, k2, k3 and k4 in the above equation. Here, the enzyme binds to the substrate; the initial complex E~S ...

### 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, ...

### 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.

### math

Let y = tan(5x+2). Find the differential dy when x = 2 and dx = 0.4 Find the differential dy when x = 2 and dx = 0.8

### Math

Let y = sqrt(7-x) Find the differential dy when x= 1 and dx = 0.4 Find the differential dy when x= 1 and dx = 0.02

### Math 1

Consider the following system of equations. y = 4x - 4 y - 4x = 3 What can you conclude about the system of equations? A) The system of equations is inconsistent. B) The system of equations is dependent. C) The system of equations is independent. D) none of these

### math

Consider the following system of equations. y = 2x - 2 y - 2x = 7 What can you conclude about the system of equations? The system of equations is inconsistent. The system of equations is dependent. The system of equations is independent. none of these

### 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) ...

### Math (Calc) (Differential Equations)

The rate of change in the number of miles s of road cleared per hour by a snowplow is inversely proportional to the depth h of snow. That is, ds/dh = k/h Find s as a function of h given that s = 25 miles when h = 3 inches and s = 10 miles when h = 9 inches (2 <= h <= 15...

### 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.

### 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: