Solution to Linear First Order ODE with Constant Coefficients/Proof 1

Proof
From the Product Rule for Derivatives:

Hence, multiplying $(1)$ all through by $e^{\int a \rd x}$:
 * $\map {\dfrac \d {\d x} } {e^{a x} y} = e^{a x} \map Q x$

Integrating $x$ now gives:
 * $\ds e^{a x} y = \int e^{a x} \map Q x \rd x + C$

whence we get the result by dividing by $e^{a x}$.