Solve dy/dx + 2y = xe^x using integrating factor

[tunabeast]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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

 

[coomast]

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]

$$\ \frac{dy}{dx} + 2y = xe^x$$
... does not seem to fit the formula layout of

Why not? What doesn't match?

 

[HallsofIvy]

Remember that p(x) and q(x) can be 'constant functions'.