\[ \left (a^2-2 a x+y(x)^2\right ) y'(x)^2+2 a y(x) y'(x)+y(x)^2=0 \] ✓ Mathematica : cpu = 8.53354 (sec), leaf count = 553
\[\left \{\text {Solve}\left [\left \{y(x)=\frac {-\sqrt {-a \text {K$\$$178361}^2 \left (a \text {K$\$$178361}^2-2 \text {K$\$$178361}^2 x-2 x\right )}-a \text {K$\$$178361}}{\text {K$\$$178361}^2+1},x=\frac {a c_1^2 \text {K$\$$178361}^2-2 a c_1 \sqrt {\text {K$\$$178361}^2+1}-2 a c_1 \text {K$\$$178361}^2 \log (\text {K$\$$178361})+2 a c_1 \text {K$\$$178361}^2 \log \left (\sqrt {\text {K$\$$178361}^2+1}+1\right )+2 a c_1 \log \left (\sqrt {\text {K$\$$178361}^2+1}+1\right )-2 a c_1 \log (\text {K$\$$178361})+a c_1^2+a \text {K$\$$178361}^2+a \text {K$\$$178361}^2 \log ^2(\text {K$\$$178361})+a \text {K$\$$178361}^2 \log ^2\left (\sqrt {\text {K$\$$178361}^2+1}+1\right )+a \log ^2\left (\sqrt {\text {K$\$$178361}^2+1}+1\right )-2 a \text {K$\$$178361}^2 \log (\text {K$\$$178361}) \log \left (\sqrt {\text {K$\$$178361}^2+1}+1\right )+2 a \sqrt {\text {K$\$$178361}^2+1} \log (\text {K$\$$178361})-2 a \log (\text {K$\$$178361}) \log \left (\sqrt {\text {K$\$$178361}^2+1}+1\right )-2 a \sqrt {\text {K$\$$178361}^2+1} \log \left (\sqrt {\text {K$\$$178361}^2+1}+1\right )+a \log ^2(\text {K$\$$178361})+a}{2 \left (\text {K$\$$178361}^2+1\right )}\right \},\{y(x),\text {K$\$$178361}\}\right ],\text {Solve}\left [\left \{y(x)=\frac {\sqrt {-a \text {K$\$$178366}^2 \left (a \text {K$\$$178366}^2-2 \text {K$\$$178366}^2 x-2 x\right )}-a \text {K$\$$178366}}{\text {K$\$$178366}^2+1},x=\frac {a c_1^2 \text {K$\$$178366}^2-2 a c_1 \sqrt {\text {K$\$$178366}^2+1}-2 a c_1 \text {K$\$$178366}^2 \log (\text {K$\$$178366})+2 a c_1 \text {K$\$$178366}^2 \log \left (\sqrt {\text {K$\$$178366}^2+1}+1\right )+2 a c_1 \log \left (\sqrt {\text {K$\$$178366}^2+1}+1\right )-2 a c_1 \log (\text {K$\$$178366})+a c_1^2+a \text {K$\$$178366}^2+a \text {K$\$$178366}^2 \log ^2(\text {K$\$$178366})+a \text {K$\$$178366}^2 \log ^2\left (\sqrt {\text {K$\$$178366}^2+1}+1\right )+a \log ^2\left (\sqrt {\text {K$\$$178366}^2+1}+1\right )-2 a \text {K$\$$178366}^2 \log (\text {K$\$$178366}) \log \left (\sqrt {\text {K$\$$178366}^2+1}+1\right )+2 a \sqrt {\text {K$\$$178366}^2+1} \log (\text {K$\$$178366})-2 a \log (\text {K$\$$178366}) \log \left (\sqrt {\text {K$\$$178366}^2+1}+1\right )-2 a \sqrt {\text {K$\$$178366}^2+1} \log \left (\sqrt {\text {K$\$$178366}^2+1}+1\right )+a \log ^2(\text {K$\$$178366})+a}{2 \left (\text {K$\$$178366}^2+1\right )}\right \},\{y(x),\text {K$\$$178366}\}\right ]\right \}\]
✓ Maple : cpu = 1.111 (sec), leaf count = 124
\[ \left \{ [x \left ( {\it \_T} \right ) ={\frac {1}{2\,a} \left ( \left ( {\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) \right ) ^{2}\sqrt {{{\it \_T}}^{2}+1}{a}^{2}-2\,{\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) \sqrt {{{\it \_T}}^{2}+1}{\it \_C1}\,a-2\,{\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) {a}^{2}+{{\it \_C1}}^{2}\sqrt {{{\it \_T}}^{2}+1}+{a}^{2}\sqrt {{{\it \_T}}^{2}+1}+2\,{\it \_C1}\,a \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}},y \left ( {\it \_T} \right ) =-{{\it \_T} \left ( a{\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) -{\it \_C1} \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}}] \right \} \]