what is the differential equation of (3x^2-2y^2)+(1-4xy)dy/dx=0

Answer 1

That is the differential equation! Now, if you want the solution, it is an exact equation, since you have

M(x,y) dx + N(x,y) dy = 0
and
∂M/∂y = ∂N/∂x = -4y

That means there is f(x,y) = c such that

f(x,y) = x^3-2xy^2 + p(y) = y - 2xy^2 + q(x)

so, p(y) = y and q(x) = x^3 and
f(x,y) = x^3-2xy^2+y = c

Answer 2

Thank you :-)