Solution to Linear First Order ODE with Constant Coefficients

Theorem
A linear first order ODE with constant coefficients in the form:
 * $(1): \quad \dfrac {\d y} {\d x} + a y = \map Q x$

has the general solution:
 * $\ds y = e^{-a x} \paren {\int e^{a x} \map Q x \rd x + C}$