# Differential Equations, implicit equation solving

1. Aug 25, 2011

### theown1

1. The problem statement, all variables and given/known data
(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.

3. 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 dont 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?

2. Aug 26, 2011

### 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.