\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {x}{y \left ( x \right ) }F \left ( -{\frac {- \left ( y \left ( x \right ) \right ) ^{2}+b}{{x}^{2}}} \right ) }=0} \]
Mathematica: cpu = 17.877770 (sec), leaf count = 233 \[ \text {Solve}\left [\int _1^{y(x)} \left (-\int _1^x \left (\frac {K[1] F\left (\frac {K[2]^2-b}{K[1]^2}\right ) \left (2 K[2] F'\left (\frac {K[2]^2-b}{K[1]^2}\right )-2 K[2]\right )}{\left (K[1]^2 F\left (\frac {K[2]^2-b}{K[1]^2}\right )-K[2]^2+b\right )^2}-\frac {2 K[2] F'\left (\frac {K[2]^2-b}{K[1]^2}\right )}{K[1] \left (K[1]^2 F\left (\frac {K[2]^2-b}{K[1]^2}\right )-K[2]^2+b\right )}\right ) \, dK[1]-\frac {K[2]}{x^2 \left (-F\left (\frac {K[2]^2-b}{x^2}\right )\right )+K[2]^2-b}\right ) \, dK[2]+\int _1^x -\frac {K[1] F\left (\frac {y(x)^2-b}{K[1]^2}\right )}{K[1]^2 F\left (\frac {y(x)^2-b}{K[1]^2}\right )+b-y(x)^2} \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.140 (sec), leaf count = 67 \[ \left \{ y \left ( x \right ) =\sqrt {{\it RootOf} \left ( -2\,\ln \left ( x \right ) +\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) -{\it \_a} \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) {x }^{2}+b},y \left ( x \right ) =-\sqrt {{\it RootOf} \left ( -2\,\ln \left ( x \right ) +\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) -{\it \_a} \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) {x }^{2}+b} \right \} \]