Second Order Non-Homogeneous

Let $D_x^2 y + p(x) D_x y + q(x)y = g(x)$ be the 2nd order non-homogeneous D.E. For simplicity, let $L[y]= D_x^2 y + p(x) D_x y + q(x)y$ (so the D.E. is $L[y] = g(x)$ ). Then the solution is of the form $y=(c_1 y_1 + c_2 y_2 = y_h) + y_p$ where $y_h$ is the solution to $L[y]=0$. To find $y_p$ there is really two methods: