Solution to Linear First Order Ordinary Differential Equation

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

has the general solution:
 * $\displaystyle y = e^{-\int P \ \mathrm d x} \left({\int Q e^{\int P \, \mathrm d x} \, \mathrm d x + C}\right)$

Also reported as
This result is also reported as:
 * $\displaystyle y e^{\int P \ \mathrm d x} = \int Q e^{\int P \, \mathrm d x} \, \mathrm d x + C$