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Chemistry LibreTexts

6.4: Problems

  • Page ID
    106837
  • 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 \(L_3(x)\)

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