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Math Help - Solving this differential equation..

  1. #1
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    Solving this differential equation..

    Please,help is very much appreciated...
    I am required to solve this second order ODE :
    y"(x)-3y'(x)-2y(x)=sinh(x)

    ....using the Variation of Parameters method.
    The final answer is EXTREMELY complicated,and i have no idea how to get to that answer.Its too long to be typed here.Would really appreciate the help.thanks.
    Note: it is a parabolic sinh(x) , not just sin(x).
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  2. #2
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    Quote Originally Posted by tite View Post
    y"(x)-3y'(x)-2y(x)=sinh(x
    Here.
    Attached Thumbnails Attached Thumbnails Solving this differential equation..-picture20.gif  
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  3. #3
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    thanks...

    thanks very much for your quick reply...
    just one more question,what if i want the solution to be in terms of sinh and cosh ? how can i transform what you gave me into such?
    thanks again.
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  4. #4
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    Quote Originally Posted by tite View Post
    thanks very much for your quick reply...
    just one more question,what if i want the solution to be in terms of sinh and cosh ? how can i transform what you gave me into such?
    thanks again.
    That is a basic integration problem, what exactly is you difficutly?

    Note that,
    e^x-e^(-x)/e^(r_1 x)
    Can be expressed as,
    e^x/e^(r_1 x) - e^(-x)/e^(r_1 x) = e^(x-r_1 x) - e^(-x-r_1x)
    Express as,
    e^(x(1-r_1))-e^(-x(1+r_1))
    You can integrate that.
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