Integrating factor
From Rice Wiki
Integrating factor is a method to solve scalar Linear First Order ODEs. It takes advantage of the product rule of derivatives
and attempts to move all y terms into the same differential order.
Note that Separation of variables is generally easier when both options are available.
Procedure
Consider a linear first order ODE.
We multiply bothsides by integrating factor such that the left hand side to be the exact derivative of a product. For this to work, we need
Applying the integrating factor, we have
From there, simple integration and algebra will solve the equation.