# Math Help - Linear Equartions!

1. ## Linear Equartions!

I am having trouble with this problem:

$x^2y'-4xy=x^7e^{x^2}+3x^5$

First step I divided by $x^2$ then I find that p(x)= -4/x and q(x)= $x^5e{x^2}+3x^2$. I that right? Well, if that is right, I am stuck at that point.

2. Works for me.

3. Can you help from that point? How do I simplify the right side which is a mess?

4. You need to solve for the integrating factor.

$y*e^{\int p(x)dx}=\int q(x)e^{\int p(x)dx}dx$

5. Yes I know but I haven't yet integrated the right side which is the G'(x) because I don't know how to start there.

6. $e^{4\int \frac{1}{x}dx}=x^4$

$y x^4= \int x^4(x^7e^{x^2}+3x^5)dx$

Break into 2 seperate integrals. For the first, integration by parts and the second is just straight forward. Lastly, divide by $x^4$