\[ y'(x)=\frac {x F\left (\frac {a y(x)^2+b x^2}{a}\right )}{\sqrt {a} y(x)} \] ✓ Mathematica : cpu = 25.3988 (sec), leaf count = 250
\[\text {Solve}\left [\int _1^{y(x)} \left (-\int _1^x \left (\frac {2 b K[1] K[2] F'\left (\frac {a K[2]^2+b K[1]^2}{a}\right )}{\sqrt {a} \left (\sqrt {a} F\left (\frac {a K[2]^2+b K[1]^2}{a}\right )+b\right )}-\frac {2 b K[1] K[2] F\left (\frac {a K[2]^2+b K[1]^2}{a}\right ) F'\left (\frac {a K[2]^2+b K[1]^2}{a}\right )}{\left (\sqrt {a} F\left (\frac {a K[2]^2+b K[1]^2}{a}\right )+b\right )^2}\right ) \, dK[1]-\frac {b K[2]}{\sqrt {a} F\left (\frac {a K[2]^2+b x^2}{a}\right )+b}\right ) \, dK[2]+\int _1^x \frac {b K[1] F\left (\frac {b K[1]^2+a y(x)^2}{a}\right )}{\sqrt {a} \left (\sqrt {a} F\left (\frac {b K[1]^2+a y(x)^2}{a}\right )+b\right )} \, dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.21 (sec), leaf count = 108
\[ \left \{ y \left ( x \right ) ={\frac {1}{a}\sqrt {a \left ( -b{x}^{2}+{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) a+b\sqrt {a} \right ) ^{-1}{d{\it \_a}}b{a}^{{\frac {3}{2}}}-b{x}^{2}+2\,{\it \_C1}\,a \right ) a \right ) }},y \left ( x \right ) =-{\frac {1}{a}\sqrt {a \left ( -b{x}^{2}+{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) a+b\sqrt {a} \right ) ^{-1}{d{\it \_a}}b{a}^{{\frac {3}{2}}}-b{x}^{2}+2\,{\it \_C1}\,a \right ) a \right ) }} \right \} \]