\[ \left (a^2-2 a x+y(x)^2\right ) y'(x)^2+2 a y(x) y'(x)+y(x)^2=0 \] ✓ Mathematica : cpu = 10.5889 (sec), leaf count = 393
\[\left \{\text {Solve}\left [\left \{y(x)=-\frac {\sqrt {-a \text {K$\$$2962283}^2 \left (a \text {K$\$$2962283}^2-2 \left (\text {K$\$$2962283}^2+1\right ) x\right )}+a \text {K$\$$2962283}}{\text {K$\$$2962283}^2+1},x=\frac {a \left (c_1^2 \text {K$\$$2962283}^2-2 c_1 \sqrt {\text {K$\$$2962283}^2+1}+2 \left (c_1 \left (\text {K$\$$2962283}^2+1\right )-\sqrt {\text {K$\$$2962283}^2+1}\right ) \log \left (\sqrt {\text {K$\$$2962283}^2+1}+1\right )+2 \log (\text {K$\$$2962283}) \left (c_1 \left (-\left (\text {K$\$$2962283}^2+1\right )\right )+\sqrt {\text {K$\$$2962283}^2+1}-\left (\text {K$\$$2962283}^2+1\right ) \log \left (\sqrt {\text {K$\$$2962283}^2+1}+1\right )\right )+c_1^2+\text {K$\$$2962283}^2+\left (\text {K$\$$2962283}^2+1\right ) \log ^2(\text {K$\$$2962283})+\left (\text {K$\$$2962283}^2+1\right ) \log ^2\left (\sqrt {\text {K$\$$2962283}^2+1}+1\right )+1\right )}{2 \left (\text {K$\$$2962283}^2+1\right )}\right \},\{y(x),\text {K$\$$2962283}\}\right ],\text {Solve}\left [\left \{y(x)=\frac {\sqrt {-a \text {K$\$$2962292}^2 \left (a \text {K$\$$2962292}^2-2 \left (\text {K$\$$2962292}^2+1\right ) x\right )}-a \text {K$\$$2962292}}{\text {K$\$$2962292}^2+1},x=\frac {a \left (c_1^2 \text {K$\$$2962292}^2-2 c_1 \sqrt {\text {K$\$$2962292}^2+1}+2 \left (c_1 \left (\text {K$\$$2962292}^2+1\right )-\sqrt {\text {K$\$$2962292}^2+1}\right ) \log \left (\sqrt {\text {K$\$$2962292}^2+1}+1\right )+2 \log (\text {K$\$$2962292}) \left (c_1 \left (-\left (\text {K$\$$2962292}^2+1\right )\right )+\sqrt {\text {K$\$$2962292}^2+1}-\left (\text {K$\$$2962292}^2+1\right ) \log \left (\sqrt {\text {K$\$$2962292}^2+1}+1\right )\right )+c_1^2+\text {K$\$$2962292}^2+\left (\text {K$\$$2962292}^2+1\right ) \log ^2(\text {K$\$$2962292})+\left (\text {K$\$$2962292}^2+1\right ) \log ^2\left (\sqrt {\text {K$\$$2962292}^2+1}+1\right )+1\right )}{2 \left (\text {K$\$$2962292}^2+1\right )}\right \},\{y(x),\text {K$\$$2962292}\}\right ]\right \}\]
✓ Maple : cpu = 1.814 (sec), leaf count = 111
\[ \left \{ [x \left ( {\it \_T} \right ) ={\frac {1}{2\,a} \left ( \left ( {\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) \right ) ^{2}\sqrt {{{\it \_T}}^{2}+1}{a}^{2}+ \left ( -2\,a{\it \_C1}\,\sqrt {{{\it \_T}}^{2}+1}-2\,{a}^{2} \right ) {\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) + \left ( {{\it \_C1}}^{2}+{a}^{2} \right ) \sqrt {{{\it \_T}}^{2}+1}+2\,a{\it \_C1} \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}},y \left ( {\it \_T} \right ) =-{{\it \_T} \left ( a{\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) -{\it \_C1} \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}}] \right \} \]