Find the general solution of each differential equation. When an initial condition is given, find the particular solution satisfying that condition.

a. \(y^{\prime \prime}-3 y^{\prime}+2 y=20 e^{-2 x}, \quad y(0)=0, \quad y^{\prime}(0)=6\).

b. \(y^{\prime \prime}+y=2 \sin 3 x\).

c. \(y^{\prime \prime}+y=1+2 \cos x\).

d. \(x^{2} y^{\prime \prime}-2 x y^{\prime}+2 y=3 x^{2}-x, \quad x>0\).