\[ \boxed { \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +a \right ) ^{2}-2\,ay \left ( x \right ) +{x}^{2}=0} \]
Mathematica: cpu = 1.713718 (sec), leaf count = 64 \[ \text {Solve}\left [\left \{y(x)=\frac {a^2+2 a \text {K$\$$1274426} x+\text {K$\$$1274426}^2 x^2+x^2}{2 a},x=\frac {c_1}{\sqrt {\text {K$\$$1274426}^2+1}}-\frac {a \sinh ^{-1}(\text {K$\$$1274426})}{\sqrt {\text {K$\$$1274426}^2+1}}\right \},\{y(x),\text {K$\$$1274426}\}\right ] \]
Maple: cpu = 7.551 (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 \} \]