\[ y'(x)=\frac {x F\left (\frac {a y(x)^2+b x^2}{a}\right )}{\sqrt {a} y(x)} \] ✓ Mathematica : cpu = 0.509152 (sec), leaf count = 253
\[\text {Solve}\left [\int _1^{y(x)}\left (-\frac {b K[2]}{b+\sqrt {a} F\left (\frac {b x^2+a K[2]^2}{a}\right )}-\int _1^x\left (\frac {2 b K[1] K[2] F'\left (\frac {b K[1]^2+a K[2]^2}{a}\right )}{\sqrt {a} \left (b+\sqrt {a} F\left (\frac {b K[1]^2+a K[2]^2}{a}\right )\right )}-\frac {2 b F\left (\frac {b K[1]^2+a K[2]^2}{a}\right ) K[1] K[2] F'\left (\frac {b K[1]^2+a K[2]^2}{a}\right )}{\left (b+\sqrt {a} F\left (\frac {b K[1]^2+a K[2]^2}{a}\right )\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {b F\left (\frac {b K[1]^2+a y(x)^2}{a}\right ) K[1]}{\sqrt {a} \left (b+\sqrt {a} F\left (\frac {b K[1]^2+a y(x)^2}{a}\right )\right )}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.245 (sec), leaf count = 108
\[y \relax (x ) = \frac {\sqrt {a \left (-b \,x^{2}+\RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right ) a +b \sqrt {a}}d \textit {\_a} \right ) b \,a^{\frac {3}{2}}-b \,x^{2}+2 c_{1} a \right ) a \right )}}{a}\]