Solve the following boundary value problems directly, when possible.

a. \(\quad x^{\prime \prime}+x=2, \quad x(0)=0, \quad x^{\prime}(1)=0\).

b. \(y^{\prime \prime}+2 y^{\prime}-8 y=0, \quad y(0)=1, \quad y(1)=0\).

c. \(y^{\prime \prime}+y=0, \quad y(0)=1, \quad y(\pi)=0\).