# Solve a differential equation

1. Mar 5, 2015

### MarkZone

1. The problem statement, all variables and given/known data
dy/dx=2xcos(y)-xy^3

2. Relevant equations

3. The attempt at a solution
dy/dx=2xcos(y)-xy^3=x(2cosy-y^3)
dy/(2cosy-y^3)=xdx

I can not integrate the left side of the equation. Can someone help me please?

Last edited: Mar 5, 2015
2. Mar 5, 2015

### SammyS

Staff Emeritus
Hello MarkZone. Welcome to PF.

Show us what you have tried, that's a requirement here.

As a small hint: Try to factor your expression.

3. Mar 6, 2015

### Staff: Mentor

@SammyS, after an edit, the OP now has separated the DE into
$$\frac{dy}{2\cos(y) - y^3} = xdx$$
I don't see how factoring sheds any light here. Maybe I'm missing something.

4. Mar 6, 2015

### SammyS

Staff Emeritus
That is separated. Right?

That was the original question.

... That is a difficult integral for sure.

5. Mar 6, 2015

### Staff: Mentor

From the thread title, the goal is to solve the DE, but in the original (unedited) post, the OP said he was not able to separate the DE. I agree that the DE is now separated, but my question pertained to how to solve the DE.

6. Mar 6, 2015

### SammyS

Staff Emeritus
Right. I agree.

I also don't see how the separation helps, unless we want a numerical solution.

7. Mar 6, 2015

### MarkZone

Thanks everyone

8. Mar 6, 2015

### LCKurtz

@MarkZone: Can you give us the context where this DE came from?

9. Mar 6, 2015

### MarkZone

Oh It was jist from my math hw. There is no context for this.

10. Mar 7, 2015

### LCKurtz

Of course there is context. What topics were you covering in your text in the section where this problem was given? What approaches were you expected to try?

11. Mar 7, 2015

### MarkZone

It is a AP calculus problem on the topic "Differential Equations & Slope fields." The original question asks me to solve this by the separation of variables method. That is all I know and my teacher does not know how to solve this either.

12. Mar 7, 2015

### SammyS

Staff Emeritus
The method of slope fields gives you a way to sketch the solutions. You don't necessarily actually find an analytic solution.