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6.4: Problems

  • Page ID
    106837
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    Problem \(\PageIndex{1}\)

    Solve the following differential equation

    \[(1-x)y'(x)-y=0 \nonumber\]

    using 1) the separation of variables method and 2) the power series method, and prove that the two solutions are mathematically equivalent.

    Problem \(\PageIndex{2}\)

    Solve the following differential equation

    \[y''(x)-y(x)=0 \nonumber\]

    using 1) the method we have learned for second order ODEs with constant coefficients and 2) the power series method, and prove that the two solutions are mathematically equivalent.

    Problem \(\PageIndex{1}\)

    Solve the Laguerre equation with \(n=2\) and \(n=3\). Write down \(L_2(x)\) and \(L_3(x)\)


    This page titled 6.4: Problems is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Marcia Levitus via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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