math285: the week of september 29

Please read the text book, Chapter 3.1-2.

The lectures are here and here.

The homework (due by Monday night):

  1. Solve
    \[
    y”+y’-2y=0.
    \]
    Answer:
    \(c_1e^t+c_2e^{-2t}\).
  2. Find the bounded solutions of
    \[
    y”=y
    \]
    such that \(y(0)=1\).

    Answer:
    \(e^{-t}\).

  3. Find general solution of
    \[
    y”-y=e^x-x^2.
    \]

    Answer:
    \(xe^{x}/2+x^2+2+c_1e^x+c_2e^{-x}\).

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