Definition:Linear First Order Ordinary Differential Equation

Definition
A linear first order ordinary differential equation is a differential equation which is in (or can be manipulated into) the form:
 * $\dfrac {dy}{dx} + P \left({x}\right) y = Q \left({x}\right)$

It is:
 * Linear because both $\dfrac {dy}{dx}$ and $y$ appear to the first power, and do not occur multiplied together;


 * First order because the highest derivative is $\dfrac {dy}{dx}$;


 * Ordinary because there are no partial derivatives occurring in it.

Its general solution is:
 * $\displaystyle y = e^{-\int P dx} \left({\int Q e^{\int P dx}dx + C}\right)$

where $C$ is an arbitrary constant.

Also see

 * Solution to Linear First Order Ordinary Differential Equation.