Chapter 4.4, Problem 42E

In Problems 41 and 42 solve the given initial-value problem in which the input function g(x) is discontinuous. [Hint: Solve each problem on two intervals, and then find a solution so that y and y′ are continuous at x = π/2 (Problem 41) and at x = π (Problem 42).]

42. y″ − 2y′ + 10y = g(x), y(0) = 0, y′(0) = 0, where $g(x)=\{\begin{array}{l}20,0\le x\le \pi \\ 0,x>\pi \end{array}$