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:
 * $\dfrac {\rd y} {\rd x} + P \left({x}\right) y = Q \left({x}\right)$

It is:


 * Linear because both $\dfrac {\rd y} {\rd x}$ and $y$ appear to the first power, and do not occur multiplied together


 * First order because the highest derivative is $\dfrac {\rd y} {\rd x}$


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

Also presented as
A linear first order ordinary differential equation can also be presented as:
 * $\dfrac {\rd y} {\rd x} = P \left({x}\right) y + Q \left({x}\right)$

Also see

 * Solution to Linear First Order Ordinary Differential Equation: Its general solution is:
 * $\displaystyle y = e^{-\int P \rd x} \left({\int Q e^{\int P \rd x} \rd x + C}\right)$

where $C$ is an arbitrary constant.