Definition:Linear First Order Ordinary Differential Equation

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

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


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


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

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

where $$C$$ is an arbitrary constant.

See Solution of Linear First Order Ordinary Differential Equation.