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Math Help - independant solution question

  1. #1
    MHF Contributor
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    independant solution question

    there is an equation (p(x)y')'+q(x)y=0 when p(x) and q(x) are deferentiable
    on I.
    y_{1}(x)=u y_{2}=\frac{1}{u(x)}
    y1 and y2 are two independant solutions of a given equation.
    show that u(x) makes a first order differential equation
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    you were given the substitution, where are you stuck?
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  3. #3
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    (p(x)u')'+q(x)u=0

    -(p(x)\frac{1}{u(x)^{2}}u')'+q(x)\frac{1}{u(x)}=0

    i put the solutions i got these two equations
    what now?
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  4. #4
    A Plied Mathematician
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    Looks good so far. Why not expand out the derivative in the second equation?
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