\[ y'(x)=\frac {x F\left (\frac {y(x)}{\sqrt {x^2+1}}\right )}{\sqrt {x^2+1}} \] ✓ Mathematica : cpu = 0.615308 (sec), leaf count = 975
\[\text {Solve}\left [\int _1^x\left (-\frac {K[1] \sqrt {K[1]^2+1} F\left (\frac {y(x)}{\sqrt {K[1]^2+1}}\right )^3}{y(x) \left (K[1]^2 F\left (\frac {y(x)}{\sqrt {K[1]^2+1}}\right )^2+F\left (\frac {y(x)}{\sqrt {K[1]^2+1}}\right )^2-y(x)^2\right )}-\frac {K[1] F\left (\frac {y(x)}{\sqrt {K[1]^2+1}}\right )^2}{K[1]^2 F\left (\frac {y(x)}{\sqrt {K[1]^2+1}}\right )^2+F\left (\frac {y(x)}{\sqrt {K[1]^2+1}}\right )^2-y(x)^2}+\frac {K[1] F\left (\frac {y(x)}{\sqrt {K[1]^2+1}}\right )}{\sqrt {K[1]^2+1} y(x)}\right )dK[1]+\int _1^{y(x)}\left (-\frac {\sqrt {x^2+1} F\left (\frac {K[2]}{\sqrt {x^2+1}}\right )}{-x^2 F\left (\frac {K[2]}{\sqrt {x^2+1}}\right )^2-F\left (\frac {K[2]}{\sqrt {x^2+1}}\right )^2+K[2]^2}-\int _1^x\left (\frac {K[1] \sqrt {K[1]^2+1} \left (\frac {2 F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right ) F'\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right ) K[1]^2}{\sqrt {K[1]^2+1}}-2 K[2]+\frac {2 F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right ) F'\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )}{\sqrt {K[1]^2+1}}\right ) F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^3}{K[2] \left (K[1]^2 F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^2+F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^2-K[2]^2\right )^2}+\frac {K[1] \sqrt {K[1]^2+1} F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^3}{K[2]^2 \left (K[1]^2 F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^2+F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^2-K[2]^2\right )}-\frac {3 K[1] F'\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right ) F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^2}{K[2] \left (K[1]^2 F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^2+F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^2-K[2]^2\right )}+\frac {K[1] \left (\frac {2 F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right ) F'\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right ) K[1]^2}{\sqrt {K[1]^2+1}}-2 K[2]+\frac {2 F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right ) F'\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )}{\sqrt {K[1]^2+1}}\right ) F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^2}{\left (K[1]^2 F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^2+F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^2-K[2]^2\right )^2}-\frac {2 K[1] F'\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right ) F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )}{\sqrt {K[1]^2+1} \left (K[1]^2 F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^2+F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )^2-K[2]^2\right )}-\frac {K[1] F\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )}{\sqrt {K[1]^2+1} K[2]^2}+\frac {K[1] F'\left (\frac {K[2]}{\sqrt {K[1]^2+1}}\right )}{\left (K[1]^2+1\right ) K[2]}\right )dK[1]-\frac {K[2]}{-x^2 F\left (\frac {K[2]}{\sqrt {x^2+1}}\right )^2-F\left (\frac {K[2]}{\sqrt {x^2+1}}\right )^2+K[2]^2}\right )dK[2]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.286 (sec), leaf count = 39
\[y \relax (x ) = \RootOf \left (-\ln \left (x^{2}+1\right )+2 \left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )-\textit {\_a}}d \textit {\_a} \right )+2 c_{1}\right ) \sqrt {x^{2}+1}\]