\[ \left (a^2-2 a x+y(x)^2\right ) y'(x)^2+2 a y(x) y'(x)+y(x)^2=0 \] ✓ Mathematica : cpu = 6.81854 (sec), leaf count = 615
\[\left \{\text {Solve}\left [\left \{y(x)=\frac {-\sqrt {-a K[1]^2 \left (a K[1]^2-2 x K[1]^2-2 x\right )}-a K[1]}{K[1]^2+1},x=\frac {a K[1]^2+a K[1]^2 \log ^2(K[1])+a \log ^2(K[1])+a K[1]^2 \log ^2\left (\sqrt {K[1]^2+1}+1\right )+a \log ^2\left (\sqrt {K[1]^2+1}+1\right )+2 a \sqrt {K[1]^2+1} \log (K[1])-2 a K[1]^2 \log (K[1]) \log \left (\sqrt {K[1]^2+1}+1\right )-2 a \log (K[1]) \log \left (\sqrt {K[1]^2+1}+1\right )-2 a \sqrt {K[1]^2+1} \log \left (\sqrt {K[1]^2+1}+1\right )+a c_1{}^2 K[1]^2-2 a c_1 \sqrt {K[1]^2+1}-2 a c_1 K[1]^2 \log (K[1])-2 a c_1 \log (K[1])+2 a c_1 K[1]^2 \log \left (\sqrt {K[1]^2+1}+1\right )+2 a c_1 \log \left (\sqrt {K[1]^2+1}+1\right )+a+a c_1{}^2}{2 \left (K[1]^2+1\right )}\right \},\{y(x),K[1]\}\right ],\text {Solve}\left [\left \{y(x)=\frac {\sqrt {-a K[2]^2 \left (a K[2]^2-2 x K[2]^2-2 x\right )}-a K[2]}{K[2]^2+1},x=\frac {a K[2]^2+a K[2]^2 \log ^2(K[2])+a \log ^2(K[2])+a K[2]^2 \log ^2\left (\sqrt {K[2]^2+1}+1\right )+a \log ^2\left (\sqrt {K[2]^2+1}+1\right )+2 a \sqrt {K[2]^2+1} \log (K[2])-2 a K[2]^2 \log (K[2]) \log \left (\sqrt {K[2]^2+1}+1\right )-2 a \log (K[2]) \log \left (\sqrt {K[2]^2+1}+1\right )-2 a \sqrt {K[2]^2+1} \log \left (\sqrt {K[2]^2+1}+1\right )+a c_1{}^2 K[2]^2-2 a c_1 \sqrt {K[2]^2+1}-2 a c_1 K[2]^2 \log (K[2])-2 a c_1 \log (K[2])+2 a c_1 K[2]^2 \log \left (\sqrt {K[2]^2+1}+1\right )+2 a c_1 \log \left (\sqrt {K[2]^2+1}+1\right )+a+a c_1{}^2}{2 \left (K[2]^2+1\right )}\right \},\{y(x),K[2]\}\right ]\right \}\] ✓ Maple : cpu = 1.39 (sec), leaf count = 111
\[\left [x \left (\textit {\_T} \right ) = \frac {\arctanh \left (\frac {1}{\sqrt {\textit {\_T}^{2}+1}}\right )^{2} \sqrt {\textit {\_T}^{2}+1}\, a^{2}+\left (-2 a c_{1} \sqrt {\textit {\_T}^{2}+1}-2 a^{2}\right ) \arctanh \left (\frac {1}{\sqrt {\textit {\_T}^{2}+1}}\right )+\left (a^{2}+c_{1}^{2}\right ) \sqrt {\textit {\_T}^{2}+1}+2 c_{1} a}{2 \sqrt {\textit {\_T}^{2}+1}\, a}, y \left (\textit {\_T} \right ) = -\frac {\left (a \arctanh \left (\frac {1}{\sqrt {\textit {\_T}^{2}+1}}\right )-c_{1}\right ) \textit {\_T}}{\sqrt {\textit {\_T}^{2}+1}}\right ]\]