How Can I Use the Slope Field Method to Solve a Differential Equation?

[MarkZone]

Homework Statement

dy/dx=2xcos(y)-xy^3[/B]

Homework Equations

The Attempt at a Solution

dy/dx=2xcos(y)-xy^3=x(2cosy-y^3)
dy/(2cosy-y^3)=xdx

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

 

[SammyS]

Homework Statement

dy/dx=2xcos(y)-xy^3[/B]

Homework Equations

The Attempt at a Solution

Can somebody help me solve this equation please? I tried to separate the variables, but it did not work.

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.

 

[Mark44]

@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.

 

[SammyS]

@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.

That is separated. Right?

That was the original question.

... That is a difficult integral for sure.

 

[Mark44]

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.

 

[SammyS]

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.

Right. I agree.

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

 

[MarkZone]

Thanks everyone

 

[LCKurtz]

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

 

[MarkZone]

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

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

 

[LCKurtz]

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

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?

 

[MarkZone]

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?

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.

 

[SammyS]

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.

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

Google "slope field method" .