Variables separable differential equations Problems and solutions

In calculus, solving the differential equations by the separation of variables is one type of math problems. The following is the list of mathematical problems with step by step procedure to learn how to solve the differential equations by the variable separable method.

Solve $y\sqrt{1-x^2}\,dy$ $+$ $x\sqrt{1-y^2}\,dx$ $\,=\,$ $0$

Solve $e^{\displaystyle x} \tan{y}\,dx$ $+$ $(1-e^{\displaystyle x})\sec^{2}{y}\,dy$ $\,=\,$ $0$

Solve $(x-y)^2\dfrac{dy}{dx}$ $\,=\,$ $a^2$