Homogeneous differential equations Problems and solutions

In calculus, the differential equations consist of homogeneous functions in some cases. It is not possible to solve the homogenous differential equations directly, but they can be solved by a special mathematical approach. The following problems are the list of homogeneous differential equations with solutions to learn how to solve homogeneous differential equations.

Solve $\dfrac{dy}{dx}$ $\,=\,$ $\dfrac{y}{x}$ $+$ $\sin{\Big(\dfrac{y}{x}\Big)}$

Solve $xy\,dx$ $-$ $(x^2+2y^2)\,dy$ $\,=\,$ $0$

Solve $xdx$ $+$ $\sin^2{\Big(\dfrac{y}{x}\Big)}(ydx-xdy)$ $\,=\,$ $0$

Solve $x^2y\,dx$ $\,=\,$ $(x^3+y^3)\,dy$