math285, week of october 6

Read the textbook, chapters 3.3 and 3.5. additional reading (highly recommended): Schoers, chapter 2.

Videos (a lot of them).

Homework (due by Tuesday, 10.14):

Solve

  1. \[
    y”’+27y=e^{-3t}+27;
    \]

    Answer: \(te^{-3t}/27+1+c_1e^{-3t}+e^{3t/2}(c_2\cos(3\sqrt{3}t/2)+c_3\sin(3\sqrt{3}t/2 )\).

  2. \[
    y^{(4)}+2y”+y=e^t;
    \]
    Answer:
    \(e^t/4+(c_1+c_2 t)\cos(t)+(c_3+c_4t)\sin(t)\).
  3. \[
    t^2y”+ty’+y=\ln(t).
    \]
  4. Answer:
    \(\ln(t)+c_1\cos(\ln(t))+c_2\sin(\ln(t))\).

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