Vyriešiť d/dxy+xsin(2y)=x^3left(cos(y)right)^2

$$\frac{d}{d x } y +x \sin ( 2y ) = { x }^{ 3 } { \left( \cos ( y ) \right) }^{ 2 }$$

Riešenie pre x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\sqrt{2\tan(y)}\text{; }x=-\sqrt{2\tan(y)}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\left(y\geq \pi n_{2}\text{ and }y<\pi n_{2}+\frac{\pi }{2}\right)\\x\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }y=\pi n_{1}+\frac{\pi }{2}\end{matrix}\right,$$

Riešenie pre y

$$\left\{\begin{matrix}\\y=\pi n_{1}+\frac{\pi }{2}\text{, }n_{1}\in \mathrm{Z}\text{; }y=\pi n_{2}+\arcsin(\frac{x^{2}}{\sqrt{x^{4}+4}})\text{, }n_{2}\in \mathrm{Z}\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right,$$