# First order differential equation

1. Feb 16, 2006

### mr bob

Just need a hand with this one.

(dy/dx)x + 2y = x^3.ln(x)

(dy/dx) = (x^3.ln(x) - 2y)/x

Integrating factor = x^2

(dy/dx)x^2 + 2xy = (x^3.ln(x))x^2

yx^2 = INT[(x^3.ln(x))x^2]

I'm having trouble integrating the last part to complete it.

Thanks alot and in advance for any help.

2. Feb 16, 2006

### Tom Mattson

Staff Emeritus
Correct.

Check this line again. You should have $x^4\ln(x)$ on the right side. You have an extra power of $x$ there.

Once you clean up the right side you should integrate by parts. If you choose wisely for the parts you will only have to do it once.

3. Feb 16, 2006

### mr bob

Thank you Tom. These differential equations can be a little tough sometimes.