october 10

Solve:

    • \[
      y”-2y’+y=te^t;
      \]
    • \[
      y”-2y’+y=t^2e^t;
      \]
    • \[
      y”-2y’+y=t^3e^t;
      \]
    • \[
      y”+y=t\sin(t);
      \]
    • \[
      y”+y=t^2\sin(t);
      \]
    • \[
      y”+y=t^3\sin(t);
      \]
    • \[
      t^2y”+ty’-4y=t^{-2};
      \]
    • \[
      t^2y”-2y=t^{-2};
      \]
    • \[
      t^2y”+ty’+y=10t^3.
      \]
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