# How to Solve First Order Differential Equations with Constant Coefficients

A differential equation of the type ${y}^{\prime }+ay=b$ can be solved by using integrating factors. This works because constants can also be functions. Since they are constants, you can use the following formula to speed up the process:

 $y=\frac{b}{a}+C\cdot {e}^{-ax}$

Example 1

Solve the differential equation ${y}^{\prime }-3y=6$

Insert the coefficients into the formula and you get

 $y=\frac{6}{-3}+C\cdot {e}^{3x}=-2+C{e}^{3x}$