\[ a y(x) \sqrt {y'(x)^2+1}-x^2-2 x y(x) y'(x)+y(x)^2=0 \] ✓ Mathematica : cpu = 21.2605 (sec), leaf count = 110
\[\left \{\left \{y(x)\to -\frac {\sqrt {a^2 c_1^2 \left (-x^2\right )-4 a^2 c_1 x-4 a^2+4 x^2}}{\sqrt {a^2 c_1^2-4}}\right \},\left \{y(x)\to \frac {\sqrt {a^2 c_1^2 \left (-x^2\right )-4 a^2 c_1 x-4 a^2+4 x^2}}{\sqrt {a^2 c_1^2-4}}\right \}\right \}\]
✓ Maple : cpu = 1.031 (sec), leaf count = 1512
\[ \left \{ \int _{{\it \_b}}^{x}\!{1 \left ( 2\,{{\it \_a}}^{3}-2\,{\it \_a}\, \left ( y \left ( x \right ) \right ) ^{2}+\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{4} \right ) } \right ) \left ( -2\,{a}^{2}{\it \_a}\, \left ( y \left ( x \right ) \right ) ^{2}+2\,{{\it \_a}}^{5}+4\,{{\it \_a}}^{3} \left ( y \left ( x \right ) \right ) ^{2}+2\, \left ( y \left ( x \right ) \right ) ^{4}{\it \_a}+{{\it \_a}}^{2}\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{4} \right ) }- \left ( y \left ( x \right ) \right ) ^{2}\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{4} \right ) } \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-{ \left ( {a}^{2}-4\,{x}^{2} \right ) {\it \_f} \left ( -2\,{a}^{2}x{{\it \_f}}^{2}+2\,{x}^{5}+4\,{x}^{3}{{\it \_f}}^{2}+2\,x{{\it \_f}}^{4}+{x}^{2}\sqrt {-{a}^{2} \left ( -{{\it \_f}}^{4}+{{\it \_f}}^{2}{a}^{2}-2\,{{\it \_f}}^{2}{x}^{2}-{x}^{4} \right ) }-{{\it \_f}}^{2}\sqrt {-{a}^{2} \left ( -{{\it \_f}}^{4}+{{\it \_f}}^{2}{a}^{2}-2\,{{\it \_f}}^{2}{x}^{2}-{x}^{4} \right ) } \right ) ^{-1}}-\int _{{\it \_b}}^{x}\!{1 \left ( -4\,{\it \_a}\,{\it \_f}-{\frac {{a}^{2} \left ( -4\,{{\it \_a}}^{2}{\it \_f}-4\,{{\it \_f}}^{3}+2\,{\it \_f}\,{a}^{2} \right ) }{2}{\frac {1}{\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) }}}} \right ) \left ( -2\,{a}^{2}{\it \_a}\,{{\it \_f}}^{2}+2\,{{\it \_a}}^{5}+4\,{{\it \_a}}^{3}{{\it \_f}}^{2}+2\,{{\it \_f}}^{4}{\it \_a}+{{\it \_a}}^{2}\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) }-{{\it \_f}}^{2}\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) } \right ) ^{-1}}-{1 \left ( 2\,{{\it \_a}}^{3}-2\,{\it \_a}\,{{\it \_f}}^{2}+\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) } \right ) \left ( -4\,{a}^{2}{\it \_a}\,{\it \_f}+8\,{{\it \_a}}^{3}{\it \_f}+8\,{\it \_a}\,{{\it \_f}}^{3}-{\frac {{a}^{2}{{\it \_a}}^{2} \left ( -4\,{{\it \_a}}^{2}{\it \_f}-4\,{{\it \_f}}^{3}+2\,{\it \_f}\,{a}^{2} \right ) }{2}{\frac {1}{\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) }}}}-2\,{\it \_f}\,\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) }+{\frac {{{\it \_f}}^{2}{a}^{2} \left ( -4\,{{\it \_a}}^{2}{\it \_f}-4\,{{\it \_f}}^{3}+2\,{\it \_f}\,{a}^{2} \right ) }{2}{\frac {1}{\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) }}}} \right ) \left ( -2\,{a}^{2}{\it \_a}\,{{\it \_f}}^{2}+2\,{{\it \_a}}^{5}+4\,{{\it \_a}}^{3}{{\it \_f}}^{2}+2\,{{\it \_f}}^{4}{\it \_a}+{{\it \_a}}^{2}\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) }-{{\it \_f}}^{2}\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) } \right ) ^{-2}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0,\int _{{\it \_b}}^{x}\!{1 \left ( 2\,{\it \_a}\, \left ( y \left ( x \right ) \right ) ^{2}-2\,{{\it \_a}}^{3}+\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{4} \right ) } \right ) \left ( 2\,{a}^{2}{\it \_a}\, \left ( y \left ( x \right ) \right ) ^{2}-2\,{{\it \_a}}^{5}-4\,{{\it \_a}}^{3} \left ( y \left ( x \right ) \right ) ^{2}-2\, \left ( y \left ( x \right ) \right ) ^{4}{\it \_a}+{{\it \_a}}^{2}\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{4} \right ) }- \left ( y \left ( x \right ) \right ) ^{2}\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2} \left ( y \left ( x \right ) \right ) ^{2}-{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{4} \right ) } \right ) ^{-1}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!{ \left ( {a}^{2}-4\,{x}^{2} \right ) {\it \_f} \left ( 2\,{a}^{2}x{{\it \_f}}^{2}-2\,{x}^{5}-4\,{x}^{3}{{\it \_f}}^{2}-2\,x{{\it \_f}}^{4}+{x}^{2}\sqrt {-{a}^{2} \left ( -{{\it \_f}}^{4}+{{\it \_f}}^{2}{a}^{2}-2\,{{\it \_f}}^{2}{x}^{2}-{x}^{4} \right ) }-{{\it \_f}}^{2}\sqrt {-{a}^{2} \left ( -{{\it \_f}}^{4}+{{\it \_f}}^{2}{a}^{2}-2\,{{\it \_f}}^{2}{x}^{2}-{x}^{4} \right ) } \right ) ^{-1}}-\int _{{\it \_b}}^{x}\!-{1 \left ( 2\,{\it \_a}\,{{\it \_f}}^{2}-2\,{{\it \_a}}^{3}+\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) } \right ) \left ( 4\,{a}^{2}{\it \_a}\,{\it \_f}-8\,{{\it \_a}}^{3}{\it \_f}-8\,{\it \_a}\,{{\it \_f}}^{3}-{\frac {{a}^{2}{{\it \_a}}^{2} \left ( -4\,{{\it \_a}}^{2}{\it \_f}-4\,{{\it \_f}}^{3}+2\,{\it \_f}\,{a}^{2} \right ) }{2}{\frac {1}{\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) }}}}-2\,{\it \_f}\,\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) }+{\frac {{{\it \_f}}^{2}{a}^{2} \left ( -4\,{{\it \_a}}^{2}{\it \_f}-4\,{{\it \_f}}^{3}+2\,{\it \_f}\,{a}^{2} \right ) }{2}{\frac {1}{\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) }}}} \right ) \left ( 2\,{a}^{2}{\it \_a}\,{{\it \_f}}^{2}-2\,{{\it \_a}}^{5}-4\,{{\it \_a}}^{3}{{\it \_f}}^{2}-2\,{{\it \_f}}^{4}{\it \_a}+{{\it \_a}}^{2}\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) }-{{\it \_f}}^{2}\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) } \right ) ^{-2}}+{1 \left ( 4\,{\it \_a}\,{\it \_f}-{\frac {{a}^{2} \left ( -4\,{{\it \_a}}^{2}{\it \_f}-4\,{{\it \_f}}^{3}+2\,{\it \_f}\,{a}^{2} \right ) }{2}{\frac {1}{\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) }}}} \right ) \left ( 2\,{a}^{2}{\it \_a}\,{{\it \_f}}^{2}-2\,{{\it \_a}}^{5}-4\,{{\it \_a}}^{3}{{\it \_f}}^{2}-2\,{{\it \_f}}^{4}{\it \_a}+{{\it \_a}}^{2}\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) }-{{\it \_f}}^{2}\sqrt {{a}^{2} \left ( {{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{{\it \_f}}^{2}+{{\it \_f}}^{4}-{{\it \_f}}^{2}{a}^{2} \right ) } \right ) ^{-1}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]