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Thread: Solutions to a given nonhomogeneous equation?

  1. Sep 24th 2009, 07:43 PM #1
    qtpipi
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    Solutions to a given nonhomogeneous equation?

    let y_p be a particular solution of the nonhomogeneous eqn y'' + py' + qy = f(x) and let y_c be a solution of its associated homogeneous eqn. show that y=y_c + y_p is a solution of the given nonhomogeneous eqn.
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  2. Sep 25th 2009, 01:01 AM #2
    chisigma
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    On the basis of your hypotheses is...

    y_{c}^{''} + p \cdot y_{c}^{'} + q\cdot y_{c} =0

    y_{p}^{''} + p \cdot y_{p}^{'} + q\cdot y_{p} = f(x)

    ... so that setting y(x)= y_{c} (x) + y_{p} (x) , because the derivative is a linear operator, you have...

    y^{''} + p \cdot y^{'} + q\cdot y = f(x)

    Kind regards

    \chi \sigma
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