Solved: In 41 and 42, solve the given initial-value problem in which the input function
Chapter 3, Problem 41(choose chapter or problem)
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 \(y^{\prime}\) are continuous at \(x=\pi / 2\) (Problem 41) and at \(x=\pi\)
(Problem 42).]
\(y^{\prime \prime}+4 y=g(x)\), y(0)=1, \(y^{\prime}(0)=2\), where
\(g(x)= \begin{cases}\sin x, & 0 \leq x \leq \pi / 2 \\ 0, & x>\pi / 2\end{cases}\)
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