We then have to face the other side of our modified differential equation and this still could be difficult or impossible to antidifferentiate.
Despite this, the method works for a number of differential equations which are reasonable models of phenomena.
Basically we build a function (called an integrating factor) with which we multiply both sides of our differential equation we wish to solve so that one side looks just like the derivative of a product of two functions.
This makes one side of the differential equation easy to anti-differentiate, but we have to address the other side of the differential equation which we just multiplied by the integrating factor.
There are modeling situations which lead to such equations and we use one involving electrical circuits to motivate the method.