1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

How to solve the ODE y'' + y = sin(x)

  1. Jul 12, 2009 #1
    1. The problem statement, all variables and given/known data
    y"+y=sinx

    initial conditions: y(90 deg) = 3, y(45 deg) = 2

    Calculate y at x = -1


    2. Relevant equations
    y=u+v


    3. The attempt at a solution

    I have gotten the following:

    r^2 + 1 = 0 Therefore, r1=i and r2 = -i

    u=(c1)cosx + (c2)sinx

    v=Asinx + Bcosx
    v'=Acosx - Bsinx
    v"=-Asinx - Bcosx

    -Asinx -Bcosx + Asinx + Bcosx - sinx = 0

    everything cancels down to: -sinx = 0. Thus, v=0

    Then I get,

    y=(c1)cosx + (c2)sinx + 0

    y(45 deg) shows that c2=2

    y(90 deg) shows that c1=3

    Thus, y=3cosx + 2sinx

    y(-1) = -.06204

    Could someone please let me know where I am making a mistake?

    Thank you in advance!
     
  2. jcsd
  3. Jul 12, 2009 #2
    Re: Differential

    The solution of the homogeneous case has terms cos x and sin x in it. The right-hand-side *also* has one of those terms in it. Presumably your textbook has the information of what to do in this exceptional case... as you found, the usual method does not work.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to solve the ODE y'' + y = sin(x)
  1. Solve Y'=x-y (Replies: 6)

  2. Y + y = sin(x) (Replies: 12)

Loading...