# Math Help - Solve the following ODE .. #3

1. ## Solve the following ODE .. #3

Problem:
Solve the following equation:
$x^4y'=-x^3y-sec(xy)$
Solution:
Rearrange:
$(x^3y+sec(xy))dx+x^4dy=0$

$sec(xy)+x^3ydx+x^4dy=0$

$sec(xy)+x^3(ydx+xdy)=0$

$sec(xy)+x^3d(xy)=0$

Devide by $sec(xy)x^3$

$x^{-3}+cos(xy)d(xy)=0$

Now, I stopped.
There is no dx with 1/x^3 so that i can integrate it!
any help?

2. I got it!
I forgot to multpily the sec(xy) by dx in the first..
so it will be:

$x^{-3} dx + cos(xy)d(xy)=0$

$\implies \dfrac{-1}{2x^2}+sin(xy)=c$