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

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