2.569   ODE No. 569

\[ \left (y'(x)^2+1\right ) \sin ^2\left (y(x)-x y'(x)\right )-1=0 \] Mathematica : cpu = 0.100249 (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 = 0.39 (sec), leaf count = 147


\[y \relax (x ) = -x \sqrt {1-x}\, \sqrt {\frac {1}{x}}-\arcsin \left (\sqrt {\frac {1}{x}}\, x \right )\]