# Thread: Differential equation

1. ## Differential equation

I need to show that this diff eq $(x+3x^3siny)dx+x^4cosy\ dy=0$ is not exact and multiply it by $\frac{1}{x}$ to make it exact..

thanks

2. Originally Posted by ashes
I need to show that this diff eq $(x+3x^3siny)dx+x^4cosy\ dy=0$ is not exact and multiply it by $\frac{1}{x}$ to make it exact..

thanks
So where are you stuck? What working can you show?

3. ## reply

for 1st part i partial diff it wrt y to get $3x^3cosy$ and 2nd part wrt x to get $4x^3cosy$...
thereafter, do I need to multiply it by x throughout to make it exact?and the general solution is just solving it like a separable diff eq right?

4. Originally Posted by ashes
for 1st part i partial diff it wrt y to get $3x^3cosy$ and 2nd part wrt x to get $4x^3cosy$...
thereafter, do I need to multiply it by x throughout to make it exact?and the general solution is just solving it like a separable diff eq right?
So you've shown it's not exact. Now you do what the quesiton tells you to do amd multiply through by 1/x (check that this makes it exact). Now solve in the usual way.