\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\sqrt {y \left ( x \right ) } \left ( \sqrt {y \left ( x \right ) }+F \left ( {\frac {x-y \left ( x \right ) }{\sqrt {y \left ( x \right ) }}} \right ) \right ) ^{-1}}=0} \]
Mathematica: cpu = 284.310103 (sec), leaf count = 271 \[ \text {Solve}\left [\int _1^{y(x)} \left (-\int _1^x -\frac {-2 \left (-\frac {K[1]-K[2]}{2 K[2]^{3/2}}-\frac {1}{\sqrt {K[2]}}\right ) \sqrt {K[2]} F'\left (\frac {K[1]-K[2]}{\sqrt {K[2]}}\right )-\frac {F\left (\frac {K[1]-K[2]}{\sqrt {K[2]}}\right )}{\sqrt {K[2]}}-1}{\left (-2 \sqrt {K[2]} F\left (\frac {K[1]-K[2]}{\sqrt {K[2]}}\right )+K[1]-K[2]\right )^2} \, dK[1]-\frac {F\left (\frac {x-K[2]}{\sqrt {K[2]}}\right )}{x \sqrt {K[2]}}+\frac {2 F\left (\frac {x-K[2]}{\sqrt {K[2]}}\right )^2+\sqrt {K[2]} F\left (\frac {x-K[2]}{\sqrt {K[2]}}\right )+x}{x \left (2 \sqrt {K[2]} F\left (\frac {x-K[2]}{\sqrt {K[2]}}\right )+K[2]-x\right )}\right ) \, dK[2]+\int _1^x \frac {1}{-2 \sqrt {y(x)} F\left (\frac {K[1]-y(x)}{\sqrt {y(x)}}\right )+K[1]-y(x)} \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.125 (sec), leaf count = 40 \[ \left \{ {\frac {\ln \left ( y \left ( x \right ) \right ) }{2}}-\int ^{ {x{\frac {1}{\sqrt {y \left ( x \right ) }}}}-\sqrt {y \left ( x \right ) }}\! \left ( 2\,F \left ( {\it \_a} \right ) -{\it \_a} \right ) ^{-1}{d{ \it \_a}}-{\it \_C1}=0 \right \} \]