Inexact differential equation
An inexact differential equation is a differential equation of the form
The solution to such equations came with the invention of the integrating factor by Leonhard Euler in 1739.In order to solve the equation, we need to transform it into an exact differential equation. In order to do that, we need to find an integrating factor to multiply the equation by. We'll start with the equation itself., so we get. We will require to satisfy. We get. After simplifying we get. Since this is a partial differential equation, it is mostly extremely hard to solve, however in some cases we will get either or, in which case we only need to find with a first-order linear differential equation or a separable differential equation, and as such either or.
