\[ \left (y'(x)^2+1\right ) \sin ^2\left (y(x)-x y'(x)\right )-1=0 \] ✓ Mathematica : cpu = 0.111325 (sec), leaf count = 59
\[\left \{\left \{y(x)\to c_1 x-\frac {1}{2} \cos ^{-1}\left (\frac {-1+c_1{}^2}{1+c_1{}^2}\right )\right \},\left \{y(x)\to c_1 x+\frac {1}{2} \cos ^{-1}\left (\frac {-1+c_1{}^2}{1+c_1{}^2}\right )\right \}\right \}\] ✓ Maple : cpu = 0.355 (sec), leaf count = 147
\[\left \{y \left (x \right ) = c_{1} x -\arcsin \left (\frac {1}{\sqrt {c_{1}^{2}+1}}\right ), y \left (x \right ) = c_{1} x +\arcsin \left (\frac {1}{\sqrt {c_{1}^{2}+1}}\right ), y \left (x \right ) = -\sqrt {-x +1}\, \sqrt {\frac {1}{x}}\, x -\arcsin \left (\sqrt {\frac {1}{x}}\, x \right ), y \left (x \right ) = \sqrt {-x +1}\, \sqrt {\frac {1}{x}}\, x +\arcsin \left (\sqrt {\frac {1}{x}}\, x \right ), y \left (x \right ) = -\sqrt {x +1}\, \sqrt {-\frac {1}{x}}\, x -\arcsin \left (\sqrt {-\frac {1}{x}}\, x \right ), y \left (x \right ) = \sqrt {x +1}\, \sqrt {-\frac {1}{x}}\, x +\arcsin \left (\sqrt {-\frac {1}{x}}\, x \right )\right \}\]