Chapter 4.8, Problem 33E

In Problems 31-34 proceed as in Example 6 to find a solution of the initial-value problem with the given piecewise-defined forcing function.

33. y″ + y = f(x), y(0) = 1, y′(0) = −1,

where $f(x)=\{\begin{array}{l}0,x<0\\ 10,0\le x\le 3\pi \\ 0,x>3\pi \end{array}$