\[ \left (a+x y'(x)\right )^2-2 a y(x)+x^2=0 \] ✓ Mathematica : cpu = 1.71343 (sec), leaf count = 64
\[\text {Solve}\left [\left \{y(x)=\frac {a^2+2 a \text {K$\$$1753755} x+\text {K$\$$1753755}^2 x^2+x^2}{2 a},x=\frac {c_1}{\sqrt {\text {K$\$$1753755}^2+1}}-\frac {a \sinh ^{-1}(\text {K$\$$1753755})}{\sqrt {\text {K$\$$1753755}^2+1}}\right \},\{y(x),\text {K$\$$1753755}\}\right ]\]
✓ Maple : cpu = 10.548 (sec), leaf count = 615
\[ \left \{ y \left ( x \right ) =-{\frac { \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) ^{4}{x}^{2}}{-2\, \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) ^{2}a-2\,a}}+2\,{\frac {{\it Arcsinh} \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) \sqrt { \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) ^{2}+1}{\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) {a}^{2}}{-2\, \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) ^{2}a-2\,a}}-{\frac { \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) ^{2}{a}^{2}}{-2\, \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) ^{2}a-2\,a}}-2\,{\frac { \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) ^{2}{x}^{2}}{-2\, \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) ^{2}a-2\,a}}-2\,{\frac {\sqrt { \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) ^{2}+1}{\it \_C1}\,{\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) a}{-2\, \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) ^{2}a-2\,a}}-{\frac {{a}^{2}}{-2\, \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) ^{2}a-2\,a}}-{\frac {{x}^{2}}{-2\, \left ( {\it RootOf} \left ( \left ( {\it Arcsinh} \left ( {\it \_Z} \right ) \right ) ^{2}{a}^{2}-{{\it \_Z}}^{2}{x}^{2}-2\,{\it Arcsinh} \left ( {\it \_Z} \right ) {\it \_C1}\,a+{{\it \_C1}}^{2}-{x}^{2} \right ) \right ) ^{2}a-2\,a}} \right \} \]