Is This First Order Differential Equation Separable or Bernoulli?

[kingkong11]

Homework Statement

Solve x²y'=1-x²+y²-x²y²

The methods I've learned so far are:
Separable, Linear, Exact, Homogeneous, and substitution for Bernoulli's D.E.

The equation is not linear, exact, or homogeneous. That leaves only two possible methods to use, separate it or get it into the form of a Bernoulli's D.E.. But I don't see how I can do that.
Anyone?

Thanks in advance!

 

[Inferior89]

Shouldn't it be separable?x^2 y'=1-x^2+y^2-x^2 y^2
x^2 y' = -(x^2-1)(y^2 + 1)

y'/(y^2 + 1) = -(x^2 - 1) / x^2

And go from there.

 

[kingkong11]

Shouldn't it be separable?


x^2 y'=1-x^2+y^2-x^2 y^2
x^2 y' = -(x^2-1)(y^2 + 1)

y'/(y^2 + 1) = -(x^2 - 1) / x^2

And go from there.

Thanks! Didn't realize I can factor the expression on the right.