What is Initial value problem: Definition and 178 Discussions

In multivariable calculus, an initial value problem[a] (ivp) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to solving an initial value problem. In that context, the differential initial value is an equation which specifies how the system evolves with time given the initial conditions of the problem.

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  1. C

    Initial Value Problem homework

    Homework Statement I'm having problems with this IVP dy/dx=y^4-x^4 and y(0)=7 I know the answer is yes but I just don't see how to get it. Homework Equations The Attempt at a Solution
  2. O

    How Do You Solve an Initial Value Problem Using Laplace Transforms?

    Laplace initial value problem... HELP! PLEASE! Hello all! I'm stuck on this question: y' + y = t sin t y(0) = 0 solve it using laplace transform,... my final is tomorrow, and its 2 am, i would appreciate a quick respone thanks in advance!
  3. J

    Second Order ODE - Initial Value Problem

    Solve the initial value problem y''+3y'+2y = 3e^{2t}+1 with initial values y(0) = 1, y'(0) = 1. I am unsure if I am going about the solution correctly. 1.) Find the characteristic equation. r^{2}+3r+2=0 \Rightarrow (r + 1)(r + 2) = 0 Therefore, y = c1•e^{-t}+c2•e^{-2t} 2.) Use method of...
  4. M

    ODE from Initial Value Problem

    Homework Statement A tank contains 3000 liters polluted water. The concentration of pollution is 5%. 50 liters per minute of the polluted water is removed and replaced with 50 liters of unpolluted water per minute. How much time will it take for the concentration to go down to 1%? 2...
  5. D

    Solve the initial value problem

    Homework Statement Solve the initial value problem given x(2)=0 \frac{dx}{dt}=tx^{2}+2x^{2}t^{2} Homework Equations The Attempt at a Solution I factored out the x^2 and separated variables and integrated as follows: \int\frac{dx}{x^{2}} = \int t+2t^{2} dt...
  6. R

    Solving the Initial Value Problem: y' = (3x^2)/[(3y^2)-4] where y(0)=1

    Im having a little issue figuring out this intial value problem. Solve the Initial Value Problem y' = (3x^2)/[(3y^2)-4] where y(0)=1 Looks like I can solve it as a seperable DE. dy/dx = (3x^2)/[(3y^2)-4] [(3y^2)-4] dy = (3x^2) dx Integrating both sides... (y^3) - 4y =...
  7. B

    Solve Initial Value Problem: dy/dt = ty(4-y)/3 with y(0) = a | Calculus Homework

    Homework Statement Hello, I am wondering if someone can look at the following: suppose I'm given an initial value problem: dy/dt = ty(4-y)/3 with y(0) = a. So, if I separable the variables, i would get: dy/4(4-y) = t/3dt and I would get by partial fractions (1/4)*lny-(1/4)ln(4-y) =...
  8. V

    Initial Value Problem for y: Solving with Calculus | Non-Zero Constant a

    Homework Statement Solve the initial value problem for y. \frac{d^2y}{dx^2}\,=\,\frac{1}{a}\sqrt{1\,+\,\left(\frac{dy}{dx}\right)^2} y(0)\,=\,a & y\prime(0)\,=\,0 a is a non-zero constant. Homework Equations The calculus. The Attempt at a Solution y\prime\,=\,sinh\,x...
  9. T

    DiffEq - Initial Value Problem / Integration help

    This question is an initial value problem for diffeq. We are asked to solve explicitly for y. (1+cos(x))dy = ((e^(-y))+1)*sin(x)dx , y(0) = 0 I attempted a separation of variables and ended up with the following: dy / ((e^(-y))+1) = (sin(x) / (1 + cos(x))) dx I know that my...
  10. S

    How to Solve an Initial-Value Problem?

    Homework Statement Solve the following initial-value problem \(y'+5y=1,\:y(1)=0\) The Attempt at a Solution y' + 5y = 0 (this is to solve for a general solution) y = -(5/2)y^2 -_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_ y' + 5y = 1 (this is for the particular solution) y = 1/5...
  11. M

    Initial Value problem with complex roots

    1.Solve the following initial value problem d^2y/dt^2 + 4y = { 1, 0<= t <=Pi/2 } {sin(t), Pi/2 < t} y(0) = 2 y'(0) = -1 I used y(t) = e^rt 3. For y'' + 4y' =1 y(t)= e^rt Yp(0)=1 r^2+4 = 0 r = 2i y1(t) = C1 Cos(2t) +...
  12. N

    Help with Initial Value Problem: Troubleshooting Integration and Antiderivatives

    I need some help with an initial value problem. It looked pretty easy at a glance, but I've ended up spending over 3 hours on this one problem.The problem is as follows: (e^(-y)+1)(sin(x) = (1+cos(x)) dy/dx With y(0) = 0. I rearranged the equation to get sin(x) / (1+cos(x)) dx = 1 /...
  13. S

    First order ODE initial value problem

    Homework Statement Given the below stated equations I need to find the exact polynomial given the initial condition. y(0) = 1 y = 4*t*sqrt(y) Homework EquationsThe Attempt at a Solution I simply disregard the initial value condition and get y = t^4 How can I find the fourth order...
  14. P

    General initial value problem (DE's)

    Homework Statement a) Consider the initial value problem \frac{dA}{dt} = kA, A(0) = A_0 as the model for the decay of a radioactive substance. Show that in general the half-life T of the substance is T = -\frac{ln2}{k} b) Show that the solution of the initial-value problem in part a) can...
  15. K

    Solving Initial Value Problem: dy/dx = 3y^(2/3) ; y(0) = 0

    Homework Statement ********************************************** Find the two solutions of the initial value problem dy/dx = 3y^(2/3) ; y(0) = 0 The attempt at a solution ********************* I integrate to find the general solution y = (x + C)^3 c=0 is obviously a...
  16. P

    Solving an Initial Value Problem: 9r^2-12r+4=0

    Solve the given initial value problem. 9y"-12y'+4y=0 y(0)=2 y'(0)=-1 9r^2-12r +4=0 (3r-2)^2 so r=2/3 so my general solution would be y(t)=c_1e^2/3t +c_2e^2/3t Whenever I try to use the initial conditions I can't get them to work. One disappears. Is my general...
  17. F

    Setting up initial value problem

    milk containing 6% fat per gallon is pumped into a tank that initially contains 300 gal of milk at 3% fat. the rate at which the milk is pumped in is 3 gal per min, whereas the mixed liquid is pumped out at the same rate. a) find the number of gallons of fat in the tank at any time. b)...
  18. T

    Solving Initial Value Problem: Finding c

    i try to solce the initial value problem question and got f(x,y) = x^2 -x +y^2 +y +c and y(0)=2 is given how do i find c?? is it just make the eqn x^2 -x +y^2 +y +c = 0 and subs y=2 and x=0?? pls help thanx
  19. K

    Initial Value Problem (with y(0) ?)

    Initial Value Problem I (kind of) understand how to do initial value problems. I know that if the problem is y' = x, y(4) = 3 then you just differentiate it, solve for y(4) and then replace the constant C (in the equation I differentiated) with this answer. But what if the initial value is...
  20. Pengwuino

    Get Help with Initial Value Problem: Solving xy' + 6y = 3xy^3 Equation

    I have a initial value problem that I have no idea how to start! Ahhh :( The equation is: xy' + 6y = 3xy^3 How do I start? I have no idea! ahhh :cry: I don't like DE's!
  21. Z

    Basic Differential Eqn - initial value problem

    The equation starts with dy/dt = ay - b, and initial condition y(0) = y_o and y_o is an arbitrary value. The book says this can be rewritten as: (dy/dt)/[y - (b/a)] = a. But I don't see how do make that step algebraically. How can the original be rewritten like that? A problem at the end of...
  22. S

    Solving an Initial Value Problem for Acceleration: Finding s at t = 1 sec

    The problem: The acceleration of a particle moving back and forth on a line is a = (d^2)s/d(t^2) = (pi)^2 cos(pi)(t) m/sec^2 for all t. If s = 0 and v = 8 m/sec when t = 0, find s when t = 1 sec. My work: (d^2)s/d(t^2) = (pi)^2 cos(pi)(t) ds/dt = (pi)^2 sin(pi)(1) + C ds/dt =...
  23. T

    Initial Value Problem question

    i was taking my final today and came across an initial value problem. Seemed pretty simple, separate the variables, integrate, then use the initial value to find the value for the constantt C. The weird thing was that the constant C would be multipled by 0 when i plug in the given initial...
  24. D

    Solving the Initial Value Problem with Euler's Method

    Consider the initial value problem y^{\prime} = \frac{3t^2}{3y^2 - 4} \mbox{,} \qquad y(1) = 0\mbox{.} (a) Use Euler's method with h=0.1 to obtain approximate values of the solution at t=1.2\mbox{, }1.4\mbox{, }1.6\mbox{, and } 1.8. (b) Repeat part (a) with h=0.05. (c) Compare the...
  25. S

    Uniqueness of Solutions for Laplace Initial Value Problems

    Hi I have to solve this equation using laplace transform ty''+(t-1)y'+y=t^2 y(0)=0 y'(0)=0 I tried it using MATLAB and get to this point (Int(-2/s^4*exp(1/2*s*(s+6)),s)+C1)*exp(-1/2*s*(s+6)) I think I've gone wrong somewhere Any Help would be appreciated. Thanks
  26. P

    Solve Initial Value Problem: dy/dx = x-4-xy-4y, y(0)=4 | Step-by-Step Guide

    \frac{dy}{dx}=x-4-xy-4y you are given that y(0)=4. so, here's what i did: \frac{dy}{dx}=(x-4)(y+1) \frac{dy}{y+1}=(x-4)dx i integrated both sides: ln(y+1)=\frac{x^2}{2}-4x+C y=e^{\frac{x^2}{2}}e^{-4x}e^{C}-1 plugged in for x and y: 4=e^{\frac{0^2}{x}}e^{-4*0}e^{C}-1 5=e^C...
  27. kreil

    Simpler way to solve differential equation for initial value problem?

    Rewrite the differential equation \frac{dy}{dx}=x{\sqrt{y}} in the form y=f(x) given the initial condition f(3)=25. I am new to integration so I am unsure about my work on this problem. \frac{dy}{dx}=x{\sqrt{y}} dy=(dx)(x)(\sqrt{y}) \frac{dy}{\sqrt{y}}=(dx)(x)...
  28. P

    How to Separate Variables in an Initial Value Problem?

    hi everyone. i need help solving this question ydx - (ytan(x/y) +x)dy = 0, where y(1) = pi/4 i know how to do the question but my problem is just i don't know how to get all the x's on one side and the y's on the other. any help would be appreciated. thanks a lot.
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