Differential Equations, implicit equation solving

[theown1]

Homework Statement

(b) Find the differential equation for which –4xy³ + 4xy³sin(x) = –1 is an implicit solution on the interval (0, pi/2). Write your answer in the form dy/dx = f (x,y) where f (x, y) depends on both x and y.

The Attempt at a Solution

I'm not too sure on how to go about solving for the differential equation after been given the implicit form. So farI got

dy/dx= cos(x)-4/(-3y³)
which I don't think is right, and


I'm not sure where to start?

(4xy³)(sin(x)-1)=-1

4y³=-1/[x(sin(x)-1]
and then do I take the derivative of this ^ to get my answer?

 

[Pi-Bond]

But the question is not even asking you to solve the equation you get; you only need to get an equation whose implicit solution is the given function. If you differentiate both sides of the given equation with respect to x (as I assume you did), you should get the required answer.