# Linear differential equation problem

## Homework Statement

$$\ \frac{dy}{dx} + 2y = xe^x$$

## The Attempt at a Solution

I'v only ever solved differential equations where values can be seperated easily, i understand i may have to use something called the integrating factor but this does not seem to fit the formula layout of

The equation you presented:

$$\frac{dy}{dx}+p(x)\cdot y=q(x)$$

is a linear differential equation of the first order. This is the next type you learn after the ones you can separate immediately. It has a general solution. What is your knowledge on the ways for solving these? You should have some idea about this, can you show an attempt of solving it?

Hurkyl
Staff Emeritus
$$\ \frac{dy}{dx} + 2y = xe^x$$