The integral curve satisfying $y' = \frac{x^2 + y^2}{x^2 - y^2}$ with $y(1) = 2$ has a slope at the point $(1, 0)$ equal to:

Prove that $x^{2}-y^{2}=c(x^{2}+y^{2})^{2}$ is the general solution of the differential equation $(x^{3}-3xy^{2})dx=(y^{3}-3x^{2}y)dy,$ where $c$ is a parameter.

The solution of the differential equation $x y^2 d y - (x^3 + y^3) d x = 0$ is

Which of the following functions are homogeneous?

If $\frac{dy}{dx} = f(x, y)$ is a homogeneous differential equation,then the general form of $f(x, y)$ is

The solution of the differential equation $\frac{dy}{dx} = -\left(\frac{x^2+3y^2}{3x^2+y^2}\right)$,$y(1)=0$ is