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Math Help - second order ODE

  1. #1
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    second order ODE

    i need some help with solving this ODE.please help! thanks.

    y"(x)=3y'(x) + 2y(x) + sinh (x)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by tite View Post
    i need some help with solving this ODE.please help! thanks.

    y"(x)=3y'(x) + 2y(x) + sinh (x)
    This an inhomegeneous linear ODE with constant cefficients.

    So if f(x) is the general solution to the homogeneous equation:

    y"(x) - 3y'(x) - 2y(x) = 0,

    and g(x) is a particular soulution of

    y"(x)=3y'(x) + 2y(x) + sinh (x)

    then the general solution is y(x) = f(x) + g(x).

    You can find a particular solution using a trail solution:

    g(x) = A sinh(x) + B cosh(x).

    Plug this into the equation and by equating coefficients of sinh and cosh
    on both sides of the equation you will end up with a pair of linear equations
    fo A and B. Which if I'm not mistaken has solution A=0, B=-1/3.

    RonL
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