\[ \boxed { a \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -x=0} \]
Mathematica: cpu = 1.013629 (sec), leaf count = 53 \[ \text {Solve}\left [\left \{x=\frac {a \text {K$\$$1210941} \sin ^{-1}(\text {K$\$$1210941})}{\sqrt {1-\text {K$\$$1210941}^2}}+\frac {c_1 \text {K$\$$1210941}}{\sqrt {1-\text {K$\$$1210941}^2}},y(x)=\frac {x}{\text {K$\$$1210941}}-a \text {K$\$$1210941}\right \},\{y(x),\text {K$\$$1210941}\}\right ] \]
Maple: cpu = 0.593 (sec), leaf count = 380 \[ \left \{ -{{\it \_C1} \left ( -y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) {\frac {1}{\sqrt {{ \frac {1}{a} \left ( -y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}+2\,a \right ) }}}}{\frac {1}{\sqrt {{ \frac {1}{a} \left ( -y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-2\,a \right ) }}}}}+x+{1 \left ( -y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{ 2}} \right ) \ln \left ( {\frac {1}{2\,a} \left ( \sqrt {{\frac {1}{{a}^ {2}} \left ( 4\,ax+2\, \left ( y \left ( x \right ) \right ) ^{2}-2\,y \left ( x \right ) \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2 }}-4\,{a}^{2} \right ) }}a+\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-y \left ( x \right ) \right ) } \right ) {\frac {1}{\sqrt {-{\frac {1}{{a}^{2}} \left ( 2\,y \left ( x \right ) \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}+4\,{a}^{2}-4\,ax-2\, \left ( y \left ( x \right ) \right ) ^{2} \right ) }}}}}=0,{{\it \_C1} \left ( y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{ 2}} \right ) {\frac {1}{\sqrt {{\frac {1}{a} \left ( -2\,y \left ( x \right ) -2\,\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}+4 \,a \right ) }}}}{\frac {1}{\sqrt {{\frac {1}{a} \left ( -2\,y \left ( x \right ) -2\,\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-4 \,a \right ) }}}}}+x-{\frac {\sqrt {2}}{2} \left ( y \left ( x \right ) + \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) \ln \left ( {\frac {1}{2\,a} \left ( \sqrt {2}\sqrt {{\frac {1}{{a}^{2}} \left ( y \left ( x \right ) \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-2\,{a}^{2}+2\,ax+ \left ( y \left ( x \right ) \right ) ^{ 2} \right ) }}a-\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}- y \left ( x \right ) \right ) } \right ) {\frac {1}{\sqrt {{\frac {1}{{a} ^{2}} \left ( y \left ( x \right ) \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-2\,{a}^{2}+2\,ax+ \left ( y \left ( x \right ) \right ) ^{2} \right ) }}}}}=0 \right \} \]