Solution to Linear First Order Ordinary Differential Equation

Theorem
A linear first order ordinary differential equation in the form:
 * $\dfrac {\d y} {\d x} + \map P x y = \map Q x$

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

Also reported as
This result is also reported as:
 * $\ds y e^{\int P \rd x} = \int Q e^{\int P \rd x} \rd x + C$

Also see

 * Solution to Linear First Order ODE with Constant Coefficients, a specific instance