Consider the problem \(y^{\prime \prime}=\sin x, y^{\prime}(0)=0, y(\pi)=0\).

a. Solve by direct integration.

b. Determine the Green's function.

c. Solve the boundary value problem using the Green's function.

d. Change the boundary conditions to \(y^{\prime}(0)=5, y(\pi)=-3\).

i. Solve by direct integration.

ii. Solve using the Green's function.