\[ a y(x) \sqrt {y'(x)^2+1}-x^2-2 x y(x) y'(x)+y(x)^2=0 \] ✓ Mathematica : cpu = 17.1699 (sec), leaf count = 110
\[\left \{\left \{y(x)\to -\frac {\sqrt {a^2 c_1{}^2 \left (-x^2\right )-4 a^2 c_1 x-4 a^2+4 x^2}}{\sqrt {-4+a^2 c_1{}^2}}\right \},\left \{y(x)\to \frac {\sqrt {a^2 c_1{}^2 \left (-x^2\right )-4 a^2 c_1 x-4 a^2+4 x^2}}{\sqrt {-4+a^2 c_1{}^2}}\right \}\right \}\] ✓ Maple : cpu = 0.833 (sec), leaf count = 1120
\[\left \{c_{1}+\int _{\textit {\_b}}^{x}\frac {2 \textit {\_a}^{3}-2 \textit {\_a} y \left (x \right )^{2}+\sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} y \left (x \right )^{2}-a^{2} y \left (x \right )^{2}+y \left (x \right )^{4}\right ) a^{2}}}{2 \textit {\_a}^{5}+4 \textit {\_a}^{3} y \left (x \right )^{2}-2 \textit {\_a} \,a^{2} y \left (x \right )^{2}+2 \textit {\_a} y \left (x \right )^{4}+\sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} y \left (x \right )^{2}-a^{2} y \left (x \right )^{2}+y \left (x \right )^{4}\right ) a^{2}}\, \textit {\_a}^{2}-\sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} y \left (x \right )^{2}-a^{2} y \left (x \right )^{2}+y \left (x \right )^{4}\right ) a^{2}}\, y \left (x \right )^{2}}d \textit {\_a} +\int _{}^{y \left (x \right )}\left (-\frac {\left (a^{2}-4 x^{2}\right ) \textit {\_f}}{2 \textit {\_f}^{4} x -2 \textit {\_f}^{2} a^{2} x +4 \textit {\_f}^{2} x^{3}+2 x^{5}-\sqrt {\textit {\_f}^{4} a^{2}+a^{2} x^{4}-\left (a^{2}-2 x^{2}\right ) \textit {\_f}^{2} a^{2}}\, \textit {\_f}^{2}+\sqrt {\textit {\_f}^{4} a^{2}+a^{2} x^{4}-\left (a^{2}-2 x^{2}\right ) \textit {\_f}^{2} a^{2}}\, x^{2}}-\left (\int _{\textit {\_b}}^{x}\frac {2 \left (-12 \textit {\_a}^{6}+\textit {\_f}^{4} a^{2}-\textit {\_f}^{2} a^{4}+\frac {\left (-2 \textit {\_a} +a \right ) \left (2 \textit {\_a} +a \right ) \left (-2 \textit {\_a}^{2}-2 \textit {\_f}^{2}+a^{2}\right ) \textit {\_a} \,\textit {\_f}^{2} a^{2}}{\sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} \textit {\_f}^{2}+\textit {\_f}^{4}-\textit {\_f}^{2} a^{2}\right ) a^{2}}}+\left (-8 \textit {\_f}^{2}+5 a^{2}\right ) \textit {\_a}^{4}+\left (4 \textit {\_f}^{4}+2 \textit {\_f}^{2} a^{2}\right ) \textit {\_a}^{2}+2 \left (-2 \textit {\_a}^{2}-2 \textit {\_f}^{2}+a^{2}\right ) \sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} \textit {\_f}^{2}+\textit {\_f}^{4}-\textit {\_f}^{2} a^{2}\right ) a^{2}}\, \textit {\_a} \right ) \textit {\_f}}{\left (-2 \textit {\_a}^{5}-4 \textit {\_a}^{3} \textit {\_f}^{2}-2 \textit {\_a} \,\textit {\_f}^{4}+2 \textit {\_a} \,\textit {\_f}^{2} a^{2}-\sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} \textit {\_f}^{2}+\textit {\_f}^{4}-\textit {\_f}^{2} a^{2}\right ) a^{2}}\, \textit {\_a}^{2}+\sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} \textit {\_f}^{2}+\textit {\_f}^{4}-\textit {\_f}^{2} a^{2}\right ) a^{2}}\, \textit {\_f}^{2}\right )^{2}}d \textit {\_a} \right )\right )d \textit {\_f} = 0, c_{1}+\int _{\textit {\_b}}^{x}\frac {-2 \textit {\_a}^{3}+2 \textit {\_a} y \left (x \right )^{2}+\sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} y \left (x \right )^{2}-a^{2} y \left (x \right )^{2}+y \left (x \right )^{4}\right ) a^{2}}}{-2 \textit {\_a}^{5}-4 \textit {\_a}^{3} y \left (x \right )^{2}+2 \textit {\_a} \,a^{2} y \left (x \right )^{2}-2 \textit {\_a} y \left (x \right )^{4}+\sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} y \left (x \right )^{2}-a^{2} y \left (x \right )^{2}+y \left (x \right )^{4}\right ) a^{2}}\, \textit {\_a}^{2}-\sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} y \left (x \right )^{2}-a^{2} y \left (x \right )^{2}+y \left (x \right )^{4}\right ) a^{2}}\, y \left (x \right )^{2}}d \textit {\_a} +\int _{}^{y \left (x \right )}\left (\frac {\left (a^{2}-4 x^{2}\right ) \textit {\_f}}{-2 \textit {\_f}^{4} x +2 \textit {\_f}^{2} a^{2} x -4 \textit {\_f}^{2} x^{3}-2 x^{5}-\sqrt {\textit {\_f}^{4} a^{2}+a^{2} x^{4}-\left (a^{2}-2 x^{2}\right ) \textit {\_f}^{2} a^{2}}\, \textit {\_f}^{2}+\sqrt {\textit {\_f}^{4} a^{2}+a^{2} x^{4}-\left (a^{2}-2 x^{2}\right ) \textit {\_f}^{2} a^{2}}\, x^{2}}-\left (\int _{\textit {\_b}}^{x}-\frac {2 \left (12 \textit {\_a}^{6}-\textit {\_f}^{4} a^{2}+\textit {\_f}^{2} a^{4}+\frac {\left (-2 \textit {\_a} +a \right ) \left (2 \textit {\_a} +a \right ) \left (-2 \textit {\_a}^{2}-2 \textit {\_f}^{2}+a^{2}\right ) \textit {\_a} \,\textit {\_f}^{2} a^{2}}{\sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} \textit {\_f}^{2}+\textit {\_f}^{4}-\textit {\_f}^{2} a^{2}\right ) a^{2}}}+\left (8 \textit {\_f}^{2}-5 a^{2}\right ) \textit {\_a}^{4}+\left (-4 \textit {\_f}^{4}-2 \textit {\_f}^{2} a^{2}\right ) \textit {\_a}^{2}+2 \left (-2 \textit {\_a}^{2}-2 \textit {\_f}^{2}+a^{2}\right ) \sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} \textit {\_f}^{2}+\textit {\_f}^{4}-\textit {\_f}^{2} a^{2}\right ) a^{2}}\, \textit {\_a} \right ) \textit {\_f}}{\left (-2 \textit {\_a}^{5}-4 \textit {\_a}^{3} \textit {\_f}^{2}-2 \textit {\_a} \,\textit {\_f}^{4}+2 \textit {\_a} \,\textit {\_f}^{2} a^{2}+\sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} \textit {\_f}^{2}+\textit {\_f}^{4}-\textit {\_f}^{2} a^{2}\right ) a^{2}}\, \textit {\_a}^{2}-\sqrt {\left (\textit {\_a}^{4}+2 \textit {\_a}^{2} \textit {\_f}^{2}+\textit {\_f}^{4}-\textit {\_f}^{2} a^{2}\right ) a^{2}}\, \textit {\_f}^{2}\right )^{2}}d \textit {\_a} \right )\right )d \textit {\_f} = 0\right \}\]