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Math Help - Finding General Solution and Initial Value Problem for Differential equation

  1. #1
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    Finding General Solution and Initial Value Problem for Differential equation

    Hi, I have the equation y''+100y = 0.5cos(10t) and I have to find the general solution and the IVP.

    For the general solution I made the y's into s's and figured out s^2 + 100 = 0 so S 1 & 2 = 0 +/- 10i

    From here I found the y-homogeneous part = k1(cos(10t))+k2(sin(10t))

    so y-particular = Acos(10t), and I found the second derivitive to equal -100Acos(10t)

    The problem is I don't know what to do next. If I plug the A's back in I get -100A+100A = 0.5 and I know this cannot be
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  2. #2
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    Re: Finding General Solution and Initial Value Problem for Differential equation

    Since the RHS of the DE is a part of the homogeneous solution, for a particular solution you should actually try $\displaystyle \begin{align*} y_p = A\,x\cos{(10t)} + B\,x\sin{(10t)} \end{align*}$.
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    Re: Finding General Solution and Initial Value Problem for Differential equation

    Quote Originally Posted by Prove It View Post
    Since the RHS of the DE is a part of the homogeneous solution, for a particular solution you should actually try $\displaystyle \begin{align*} y_p = A\,x\cos{(10t)} + B\,x\sin{(10t)} \end{align*}$.
    Typo: obviously, this should be y_p= At cos(10t)+ Bt sin(10t).
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    Re: Finding General Solution and Initial Value Problem for Differential equation

    Quote Originally Posted by HallsofIvy View Post
    Typo: obviously, this should be y_p= At cos(10t)+ Bt sin(10t).
    Yes, these interchangeable letters they have for independent variables :P hahaha.
    Last edited by topsquark; April 24th 2014 at 11:54 AM.
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