\[ \boxed { \left ( \left ( y \left ( x \right ) \right ) ^{2}-2\,ax+{a}^{2} \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+2\,ay \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 8.600592 (sec), leaf count = 553 \[ \left \{\text {Solve}\left [\left \{y(x)=\frac {-\sqrt {-a \text {K$\$$1287907}^2 \left (a \text {K$\$$1287907}^2-2 \text {K$\$$1287907}^2 x-2 x\right )}-a \text {K$\$$1287907}}{\text {K$\$$1287907}^2+1},x=\frac {a c_1^2 \text {K$\$$1287907}^2-2 a c_1 \sqrt {\text {K$\$$1287907}^2+1}-2 a c_1 \text {K$\$$1287907}^2 \log (\text {K$\$$1287907})+2 a c_1 \text {K$\$$1287907}^2 \log \left (\sqrt {\text {K$\$$1287907}^2+1}+1\right )+2 a c_1 \log \left (\sqrt {\text {K$\$$1287907}^2+1}+1\right )-2 a c_1 \log (\text {K$\$$1287907})+a c_1^2+a \text {K$\$$1287907}^2+a \text {K$\$$1287907}^2 \log ^2(\text {K$\$$1287907})+a \text {K$\$$1287907}^2 \log ^2\left (\sqrt {\text {K$\$$1287907}^2+1}+1\right )+a \log ^2\left (\sqrt {\text {K$\$$1287907}^2+1}+1\right )-2 a \text {K$\$$1287907}^2 \log (\text {K$\$$1287907}) \log \left (\sqrt {\text {K$\$$1287907}^2+1}+1\right )+2 a \sqrt {\text {K$\$$1287907}^2+1} \log (\text {K$\$$1287907})-2 a \log (\text {K$\$$1287907}) \log \left (\sqrt {\text {K$\$$1287907}^2+1}+1\right )-2 a \sqrt {\text {K$\$$1287907}^2+1} \log \left (\sqrt {\text {K$\$$1287907}^2+1}+1\right )+a \log ^2(\text {K$\$$1287907})+a}{2 \left (\text {K$\$$1287907}^2+1\right )}\right \},\{y(x),\text {K$\$$1287907}\}\right ],\text {Solve}\left [\left \{y(x)=\frac {\sqrt {-a \text {K$\$$1287912}^2 \left (a \text {K$\$$1287912}^2-2 \text {K$\$$1287912}^2 x-2 x\right )}-a \text {K$\$$1287912}}{\text {K$\$$1287912}^2+1},x=\frac {a c_1^2 \text {K$\$$1287912}^2-2 a c_1 \sqrt {\text {K$\$$1287912}^2+1}-2 a c_1 \text {K$\$$1287912}^2 \log (\text {K$\$$1287912})+2 a c_1 \text {K$\$$1287912}^2 \log \left (\sqrt {\text {K$\$$1287912}^2+1}+1\right )+2 a c_1 \log \left (\sqrt {\text {K$\$$1287912}^2+1}+1\right )-2 a c_1 \log (\text {K$\$$1287912})+a c_1^2+a \text {K$\$$1287912}^2+a \text {K$\$$1287912}^2 \log ^2(\text {K$\$$1287912})+a \text {K$\$$1287912}^2 \log ^2\left (\sqrt {\text {K$\$$1287912}^2+1}+1\right )+a \log ^2\left (\sqrt {\text {K$\$$1287912}^2+1}+1\right )-2 a \text {K$\$$1287912}^2 \log (\text {K$\$$1287912}) \log \left (\sqrt {\text {K$\$$1287912}^2+1}+1\right )+2 a \sqrt {\text {K$\$$1287912}^2+1} \log (\text {K$\$$1287912})-2 a \log (\text {K$\$$1287912}) \log \left (\sqrt {\text {K$\$$1287912}^2+1}+1\right )-2 a \sqrt {\text {K$\$$1287912}^2+1} \log \left (\sqrt {\text {K$\$$1287912}^2+1}+1\right )+a \log ^2(\text {K$\$$1287912})+a}{2 \left (\text {K$\$$1287912}^2+1\right )}\right \},\{y(x),\text {K$\$$1287912}\}\right ]\right \} \]
Maple: cpu = 1.341 (sec), leaf count = 124 \[ \left \{ [x \left ( {\it \_T} \right ) ={\frac {1}{2\,a} \left ( \left ( {\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) \right ) ^{2}\sqrt {{{\it \_T}}^{2}+1}{a}^{2}-2\,{\it Artanh} \left ( { \frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) \sqrt {{{\it \_T}}^{2}+1 }{\it \_C1}\,a-2\,{\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2 }+1}}} \right ) {a}^{2}+\sqrt {{{\it \_T}}^{2}+1}{{\it \_C1}}^{2}+{a}^{ 2}\sqrt {{{\it \_T}}^{2}+1}+2\,{\it \_C1}\,a \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}},y \left ( {\it \_T} \right ) =-{{\it \_T} \left ( a{\it Artanh} \left ( {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}} \right ) -{ \it \_C1} \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}}] \right \} \]