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

Proof
From the Product Rule for Derivatives:

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

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

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