Combination of Solutions to Non-Homogeneous LSOODE with same Homogeneous Part

Theorem
Let $\map {y_1} x$ be a particular solution of the linear second order ODE:
 * $(1): \quad y'' + \map P x y' + \map Q x y = \map {R_1} x$

Let $\map {y_2} x$ be a particular solution of the linear second order ODE:
 * $(2): \quad y'' + \map P x y' + \map Q x y = \map {R_2} x$

Then $\map y x = \map {y_1} x + \map {y_2} x$ is a particular solution of the linear second order ODE:
 * $(3): \quad y'' + \map P x y' + \map Q x y = \map {R_1} x + \map {R_2} x$

Proof
Hence the result.