Laplace transform \( y^{\prime}+y=f(t) \) with \( y(0)=2 \), where \( f(t)=\left\{\begin{array}{ll}0 & 0 \leq t

Question

Solve the differential equation using Laplace transforms

\( y^{\prime}+y=f(t) \) with \( y(0)=2 \), where \( f(t)=\left\{\begin{array}{ll}0 & 0 \leq t<\pi / 2 \\ \cos t & t \geq \pi / 2\end{array}\right. \)