2.569   ODE No. 569

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

$$(y^{\prime }(x{)}^2+1){\sin }^2(y(x)-x{y}^{\prime }(x))-1=0$$ ✓ Mathematica : cpu = 0.0885836 (sec), leaf count = 59

$$\{\{y(x)\to c_{1}x-\frac{1}{2}{\cos }^{-1}\left(\frac{-1+c_1{}^2}{1+c_1{}^2}\right)\},\{y(x)\to c_{1}x+\frac{1}{2}{\cos }^{-1}\left(\frac{-1+c_1{}^2}{1+c_1{}^2}\right)\}\}$$ ✓ Maple : cpu = 0.676 (sec), leaf count = 147

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x-\arcsin \left(\frac{1}{\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+1}}\right),y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x+\arcsin \left(\frac{1}{\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+1}}\right),y\left(x\right)=-x\sqrt{1-x}\sqrt{x^{-1}}-\arcsin \left(\sqrt{x^{-1}}x\right),y\left(x\right)=x\sqrt{1-x}\sqrt{x^{-1}}+\arcsin \left(\sqrt{x^{-1}}x\right),y\left(x\right)=-x\sqrt{1+x}\sqrt{-x^{-1}}-\arcsin \left(\sqrt{-x^{-1}}x\right),y\left(x\right)=x\sqrt{1+x}\sqrt{-x^{-1}}+\arcsin \left(\sqrt{-x^{-1}}x\right)\}$$