1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solve the differential equation

  1. Nov 22, 2009 #1
    1. The problem statement, all variables and given/known data
    a.Find solution to the differential equation
    dy/dx=cos(x^2)*exp(sin(x));y(0)=0 for x in the interval [0,10]
    b.find y(10)

    2. Relevant equations

    3. The attempt at a solution
    I don't know where to begin
  2. jcsd
  3. Nov 22, 2009 #2
    That differential equation is separable.
  4. Nov 22, 2009 #3
    I got:
    y = cos(x^2)*exp(sin(x))
    integral(y) = integral(cos(x^2)*exp(sin(x)))
    I got stuck. What do I need to do next
  5. Nov 22, 2009 #4


    Staff: Mentor

    After separation you should have
    [tex]\int dy~=~\int cos(x^2)e^{sin(x)}dx[/tex]

    Now is a good time to verify that you have given us the correct differential equation.
  6. Nov 22, 2009 #5
    I actually use ODE45 in matlab to solve the equation and plot it simultaneously.
    I tried to integrate the equation using 'int' command but it did not work.
    I have no clue how to solve it with only one variable on the right hand side because to solve the separable differential equation you need x and y.
  7. Nov 22, 2009 #6
    are u sure this is the right differential equation?

    u get [tex]Y =~\int cos(x^2)e^{sin(x)}dx[/tex]

    but i enter the right side in mathematica and get no result
  8. Nov 22, 2009 #7
    I am positive. The original equation is dy/dx = cos(x^2)*exp(sin(x))
  9. Nov 22, 2009 #8


    Staff: Mentor

    For the a part,
    [tex]y(x)~=~\int_{t = 0}^{x} cos(t^2)e^{sin(t)}dt[/tex]

    For the b part,
    [tex]\int_{x = 0}^{10} dy~=~\int_{x = 0}^{10} cos(x^2)e^{sin(x)}dx[/tex]
    [tex]\Rightarrow y(10) - y(0)~=~\int_{x = 0}^{10} cos(x^2)e^{sin(x)}dx[/tex]
    Since y(0) = 0, then
    [tex]y(10)~=~\int_{x = 0}^{10} cos(x^2)e^{sin(x)}dx[/tex]

    I don't think you can do much more with this if the exact solution is what is wanted.
  10. Nov 22, 2009 #9
    But how can I find y(10)
  11. Nov 22, 2009 #10


    Staff: Mentor

    Look in post #9. There it is.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook