#### 2.569   ODE No. 569

$\left (y'(x)^2+1\right ) \sin ^2\left (y(x)-x y'(x)\right )-1=0$ Mathematica : cpu = 0.0927792 (sec), leaf count = 59

$\left \{\left \{y(x)\to c_1 x-\frac {1}{2} \cos ^{-1}\left (\frac {c_1{}^2-1}{c_1{}^2+1}\right )\right \},\left \{y(x)\to c_1 x+\frac {1}{2} \cos ^{-1}\left (\frac {c_1{}^2-1}{c_1{}^2+1}\right )\right \}\right \}$ Maple : cpu = 0.306 (sec), leaf count = 147

$\left \{ y \left ( x \right ) =x{\it \_C1}-\arcsin \left ( {\frac {1}{\sqrt {{{\it \_C1}}^{2}+1}}} \right ) ,y \left ( x \right ) =x{\it \_C1}+\arcsin \left ( {\frac {1}{\sqrt {{{\it \_C1}}^{2}+1}}} \right ) ,y \left ( x \right ) =-x\sqrt {1-x}\sqrt {{x}^{-1}}-\arcsin \left ( \sqrt {{x}^{-1}}x \right ) ,y \left ( x \right ) =x\sqrt {1-x}\sqrt {{x}^{-1}}+\arcsin \left ( \sqrt {{x}^{-1}}x \right ) ,y \left ( x \right ) =-x\sqrt {1+x}\sqrt {-{x}^{-1}}-\arcsin \left ( \sqrt {-{x}^{-1}}x \right ) ,y \left ( x \right ) =x\sqrt {1+x}\sqrt {-{x}^{-1}}+\arcsin \left ( \sqrt {-{x}^{-1}}x \right ) \right \}$