# What is a solution to the differential equation #dy/dx=(2y+x^2)/x#?

##### 2 Answers

#### Explanation:

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

(https://en.wikipedia.org/wiki/Joseph-Louis_de_Lagrange)

called the constant variation technique.

We will suppose that

#### Explanation:

Alternative Approach

This is **exact** if we times it by a factor of

ie

**Integrating Factor**

We can extract the "integrating factor"