Linear Second Order ODE/y'' = y'/Proof 2

Proof
Using Solution of Second Order Differential Equation with Missing Independent Variable, $(1)$ can be expressed as:

$(1)$ is a linear first order ODE in the form:
 * $\dfrac {\d y} {\d x} + \map P x y = \map Q x$

where:
 * $\map P x = -1$
 * $\map Q x = -A_2$

Thus:

Thus from Solution by Integrating Factor, $(1)$ can be rewritten as: