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Math Help - solve given a yh1

  1. #1
    Member pberardi's Avatar
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    solve given a yh1

    Hello,
    I cannot for the life of me remember how to do this. Can someone help please?

    Solve the following differential equation xy''+y'=12x^2 given that yh1 = 1 is a solution of the homogeneous equation.

    Thanks.
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  2. #2
    MHF Contributor chisigma's Avatar
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    The procedure to arrive, once you know a solution of this type of equation, to a second solution independent from it, is illustrated here...

    http://www.mathhelpforum.com/math-help/calculus/82519-variation-parameter-2nd-order-ode.html

    Kind regards

    \chi \sigma
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  3. #3
    MHF Contributor Calculus26's Avatar
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    Normally this could be handled using reduction of order where we would make the substitution:

    y(x) = yh*z(x)

    However since yh = 1 we don't need to do this

    Let z = y ' directly and we have

    xz' + z =12x^2

    (xz) ' =12x^2

    xz = 4x^3 + C1

    z = 4x^2 +C1/x Note 1/x is the other homogeneous solution

    now solve y ' = 4x^2 +C1/x
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