Differential Equations by separation of variables

[LAK]

Can someone please help me to calculate the following using separation of variables:

dy/dx = x*(1 - y^2)^(1/2)

to that the solution is in the form:

y =

 

[MarkFL]

I have moved both your threads here to the Differential Equations subforum as this is a better fit for them.

What do you get when you separate the variables, before integrating?

 

[Prove It]

Can someone please help me to calculate the following using separation of variables:

dy/dx = x*(1 - y^2)^(1/2)

to that the solution is in the form:

y =

For starters:

$\displaystyle \begin{align*} \frac{1}{\sqrt{1 - y^2}} \, \frac{dy}{dx} = x \end{align*}$

and now you can integrate both side w.r.t. x :)