What is a solution to the differential equation #dy/dx=(2y+x^2)/x#?
This is a linear differential equation. Its solution can be composed of the homogeneous solution (
The homogeneous solution obeys
By grouping variables:
The determination of
To solve this, we will use a technique due to Lagrange
called the constant variation technique.
We will suppose that
This is exact if we times it by a factor of
We can extract the "integrating factor"