First Order Linear Differential Equation

A Linear Differential Equation of Order 1. We are assuming it to be a Ordinary Differential Equation.

Techniques

Integrating Factor

If and only if The given equation is a First Order Linear Differential Equation and the coefficient of the first order derivative is 1, i.e. in the given form

Then it is possible to simplify the process of solving the equation by multiplying both sides of the equation by some function

Then let , and you now have a product rule that when integrated and after some algebra gives an explicit solution for so long as you can solve for whatever needs to be.

Example