3.354   ODE No. 354

$$\boxed{{\displaystyle (x\sin \left(y\left(x\right)\right)-1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+\cos \left(y\left(x\right)\right)=0}}$$

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

Mathematica: cpu = 0.064008 (sec), leaf count = 145 $$\{\{y(x)\to -{\cos }^{-1}\left(\frac{c_{1}x-\sqrt{c_1^2-x^2+1}}{c_1^2+1}\right)\},\{y(x)\to {\cos }^{-1}\left(\frac{c_{1}x-\sqrt{c_1^2-x^2+1}}{c_1^2+1}\right)\},\{y(x)\to -{\cos }^{-1}\left(\frac{\sqrt{c_1^2-x^2+1}+c_{1}x}{c_1^2+1}\right)\},\{y(x)\to {\cos }^{-1}\left(\frac{\sqrt{c_1^2-x^2+1}+c_{1}x}{c_1^2+1}\right)\}\}$$

Maple: cpu = 0.047 (sec), leaf count = 115 $$\{y\left(x\right)=\arctan (\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\mathit{\_}\mathit{C}\mathit{1}}^2+1}(-\mathit{\_}\mathit{C}\mathit{1}x+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2-x^2+1})+x,-\frac{1}{{\mathit{\_}\mathit{C}\mathit{1}}^2+1}(-\mathit{\_}\mathit{C}\mathit{1}x+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2-x^2+1})),y\left(x\right)=\arctan (-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\mathit{\_}\mathit{C}\mathit{1}}^2+1}(\mathit{\_}\mathit{C}\mathit{1}x+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2-x^2+1})+x,\frac{1}{{\mathit{\_}\mathit{C}\mathit{1}}^2+1}(\mathit{\_}\mathit{C}\mathit{1}x+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2-x^2+1}))\}$$