3.351   ODE No. 351

$$\boxed{{\displaystyle \left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)\cos \left(y\left(x\right)\right)+x\sin \left(y\left(x\right)\right){(\cos \left(y\left(x\right)\right))}^2-{(\sin \left(y\left(x\right)\right))}^3=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.367047 (sec), leaf count = 61 $$\{\{y(x)\to -{\cot }^{-1}\left(\sqrt{e^{x^2}(4c_1-\sqrt{\pi }\text{erf}(x))}\right)\},\{y(x)\to {\cot }^{-1}\left(\sqrt{e^{x^2}(4c_1-\sqrt{\pi }\text{erf}(x))}\right)\}\}$$

Maple: cpu = 0.343 (sec), leaf count = 55 $$\{y\left(x\right)=-\arcsin \left(\frac{1}{\sqrt{1-\sqrt{\pi }\mathit{E}\mathit{r}\mathit{f}\left(x\right){\mathrm{e}}^{x^2}-2\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{x^2}}}\right),y\left(x\right)=\arcsin \left(\frac{1}{\sqrt{1-\sqrt{\pi }\mathit{E}\mathit{r}\mathit{f}\left(x\right){\mathrm{e}}^{x^2}-2\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{x^2}}}\right)\}$$