\[ \left (a^2-2 a x+y(x)^2\right ) y'(x)^2+2 a y(x) y'(x)+y(x)^2=0 \] ✓ Mathematica : cpu = 8.45994 (sec), leaf count = 553
\[\left \{\text {Solve}\left [\left \{y(x)=\frac {-\sqrt {-a \text {K$\$$1786906}^2 \left (a \text {K$\$$1786906}^2-2 \text {K$\$$1786906}^2 x-2 x\right )}-a \text {K$\$$1786906}}{\text {K$\$$1786906}^2+1},x=\frac {a c_1^2 \text {K$\$$1786906}^2-2 a c_1 \sqrt {\text {K$\$$1786906}^2+1}-2 a c_1 \text {K$\$$1786906}^2 \log (\text {K$\$$1786906})+2 a c_1 \text {K$\$$1786906}^2 \log \left (\sqrt {\text {K$\$$1786906}^2+1}+1\right )+2 a c_1 \log \left (\sqrt {\text {K$\$$1786906}^2+1}+1\right )-2 a c_1 \log (\text {K$\$$1786906})+a c_1^2+a \text {K$\$$1786906}^2+a \text {K$\$$1786906}^2 \log ^2(\text {K$\$$1786906})+a \text {K$\$$1786906}^2 \log ^2\left (\sqrt {\text {K$\$$1786906}^2+1}+1\right )+a \log ^2\left (\sqrt {\text {K$\$$1786906}^2+1}+1\right )-2 a \text {K$\$$1786906}^2 \log (\text {K$\$$1786906}) \log \left (\sqrt {\text {K$\$$1786906}^2+1}+1\right )+2 a \sqrt {\text {K$\$$1786906}^2+1} \log (\text {K$\$$1786906})-2 a \log (\text {K$\$$1786906}) \log \left (\sqrt {\text {K$\$$1786906}^2+1}+1\right )-2 a \sqrt {\text {K$\$$1786906}^2+1} \log \left (\sqrt {\text {K$\$$1786906}^2+1}+1\right )+a \log ^2(\text {K$\$$1786906})+a}{2 \left (\text {K$\$$1786906}^2+1\right )}\right \},\{y(x),\text {K$\$$1786906}\}\right ],\text {Solve}\left [\left \{y(x)=\frac {\sqrt {-a \text {K$\$$1786911}^2 \left (a \text {K$\$$1786911}^2-2 \text {K$\$$1786911}^2 x-2 x\right )}-a \text {K$\$$1786911}}{\text {K$\$$1786911}^2+1},x=\frac {a c_1^2 \text {K$\$$1786911}^2-2 a c_1 \sqrt {\text {K$\$$1786911}^2+1}-2 a c_1 \text {K$\$$1786911}^2 \log (\text {K$\$$1786911})+2 a c_1 \text {K$\$$1786911}^2 \log \left (\sqrt {\text {K$\$$1786911}^2+1}+1\right )+2 a c_1 \log \left (\sqrt {\text {K$\$$1786911}^2+1}+1\right )-2 a c_1 \log (\text {K$\$$1786911})+a c_1^2+a \text {K$\$$1786911}^2+a \text {K$\$$1786911}^2 \log ^2(\text {K$\$$1786911})+a \text {K$\$$1786911}^2 \log ^2\left (\sqrt {\text {K$\$$1786911}^2+1}+1\right )+a \log ^2\left (\sqrt {\text {K$\$$1786911}^2+1}+1\right )-2 a \text {K$\$$1786911}^2 \log (\text {K$\$$1786911}) \log \left (\sqrt {\text {K$\$$1786911}^2+1}+1\right )+2 a \sqrt {\text {K$\$$1786911}^2+1} \log (\text {K$\$$1786911})-2 a \log (\text {K$\$$1786911}) \log \left (\sqrt {\text {K$\$$1786911}^2+1}+1\right )-2 a \sqrt {\text {K$\$$1786911}^2+1} \log \left (\sqrt {\text {K$\$$1786911}^2+1}+1\right )+a \log ^2(\text {K$\$$1786911})+a}{2 \left (\text {K$\$$1786911}^2+1\right )}\right \},\{y(x),\text {K$\$$1786911}\}\right ]\right \}\]
✓ Maple : cpu = 1.113 (sec), leaf count = 111
\[ \left \{ [x \left ( {\it \_T} \right ) ={\frac {1}{2\,a} \left ( \left ( {\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) \right ) ^{2}\sqrt {{{\it \_T}}^{2}+1}{a}^{2}+ \left ( -2\,a{\it \_C1}\,\sqrt {{{\it \_T}}^{2}+1}-2\,{a}^{2} \right ) {\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) + \left ( {{\it \_C1}}^{2}+{a}^{2} \right ) \sqrt {{{\it \_T}}^{2}+1}+2\,{\it \_C1}\,a \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}},y \left ( {\it \_T} \right ) =-{{\it \_T} \left ( a{\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) -{\it \_C1} \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}}] \right \} \]