2.350   ODE No. 350

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

$$y^{\prime }(x)\cos (y(x))-\sin (y(x))-\cos (x){\sin }^2(y(x))=0$$ ✓ Mathematica : cpu = 0.550197 (sec), leaf count = 53

$$\{\{y(x)\to {\csc }^{-1}\left(\frac{1}{2}(-\sin (x)-\cos (x)-2c_1{e}^{-x})\right)\},\{y(x)\to -{\csc }^{-1}\left(\frac{1}{2}(\sin (x)+\cos (x)+2c_1{e}^{-x})\right)\}\}$$ ✓ Maple : cpu = 0.772 (sec), leaf count = 226

$$\{y\left(x\right)=\arctan (-2\frac{{\mathrm{e}}^x}{{\mathrm{e}}^x(\cos \left(x\right)+\sin \left(x\right))+2\mathit{\_}\mathit{C}\mathit{1}},\frac{\sqrt{16}}{4{\mathit{\_}\mathit{C}\mathit{1}}^2+4{\mathrm{e}}^x(\cos \left(x\right)+\sin \left(x\right))\mathit{\_}\mathit{C}\mathit{1}+{\left({\mathrm{e}}^x\right)}^2(2\cos \left(x\right)\sin \left(x\right)+1)}\sqrt{((\frac{\cos \left(x\right)\sin \left(x\right)}{2}-\frac{3}{4}){\left({\mathrm{e}}^x\right)}^2+{\mathrm{e}}^x(\cos \left(x\right)+\sin \left(x\right))\mathit{\_}\mathit{C}\mathit{1}+{\mathit{\_}\mathit{C}\mathit{1}}^2)((\frac{\cos \left(x\right)\sin \left(x\right)}{2}+\frac{1}{4}){\left({\mathrm{e}}^x\right)}^2+{\mathrm{e}}^x(\cos \left(x\right)+\sin \left(x\right))\mathit{\_}\mathit{C}\mathit{1}+{\mathit{\_}\mathit{C}\mathit{1}}^2)}),y\left(x\right)=\arctan (-2\frac{{\mathrm{e}}^x}{{\mathrm{e}}^x(\cos \left(x\right)+\sin \left(x\right))+2\mathit{\_}\mathit{C}\mathit{1}},-\frac{\sqrt{16}}{4{\mathit{\_}\mathit{C}\mathit{1}}^2+4{\mathrm{e}}^x(\cos \left(x\right)+\sin \left(x\right))\mathit{\_}\mathit{C}\mathit{1}+{\left({\mathrm{e}}^x\right)}^2(2\cos \left(x\right)\sin \left(x\right)+1)}\sqrt{((\frac{\cos \left(x\right)\sin \left(x\right)}{2}-\frac{3}{4}){\left({\mathrm{e}}^x\right)}^2+{\mathrm{e}}^x(\cos \left(x\right)+\sin \left(x\right))\mathit{\_}\mathit{C}\mathit{1}+{\mathit{\_}\mathit{C}\mathit{1}}^2)((\frac{\cos \left(x\right)\sin \left(x\right)}{2}+\frac{1}{4}){\left({\mathrm{e}}^x\right)}^2+{\mathrm{e}}^x(\cos \left(x\right)+\sin \left(x\right))\mathit{\_}\mathit{C}\mathit{1}+{\mathit{\_}\mathit{C}\mathit{1}}^2)})\}$$