4.1.4. First order linear differential equations

A linear first-order equation is an equation that is linear with respect to the function y and its derivative y ' .

It looks like:

y ' = p ( x ) · y + q ( x ),
where p ( x ) and q ( x ) are given continuous or constant functions.

The solution of the linear equation is sought in the form y = u ( x ) · v ( x ) . The functions u ( x ) and v ( x ) are found from equations with separable variables:
a) v ' = p ( x ) · v ;
b) u '· v ( x ) = q ( x ) .