\[ a y'(x)^2-y(x) y'(x)-x=0 \] ✓ Mathematica : cpu = 0.805152 (sec), leaf count = 49
\[\text {Solve}\left [\left \{x=\frac {a \text {K$\$$1239384} \sinh ^{-1}(\text {K$\$$1239384})}{\sqrt {\text {K$\$$1239384}^2+1}}+\frac {c_1 \text {K$\$$1239384}}{\sqrt {\text {K$\$$1239384}^2+1}},y(x)=a \text {K$\$$1239384}-\frac {x}{\text {K$\$$1239384}}\right \},\{y(x),\text {K$\$$1239384}\}\right ]\]
✓ Maple : cpu = 0.081 (sec), leaf count = 266
\[ \left \{ {{\it \_C1} \left ( -y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) {\frac {1}{\sqrt {-{\frac {1}{{a}^{2}} \left ( 2\,y \left ( x \right ) \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-4\,{a}^{2}-4\,ax-2\, \left ( y \left ( x \right ) \right ) ^{2} \right ) }}}}}+x-{1 \left ( -y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) {\it Arcsinh} \left ( {\frac {1}{2\,a} \left ( -y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) } \right ) {\frac {1}{\sqrt {-{\frac {1}{{a}^{2}} \left ( 2\,y \left ( x \right ) \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}-4\,{a}^{2}-4\,ax-2\, \left ( y \left ( x \right ) \right ) ^{2} \right ) }}}}}=0,{{\it \_C1} \left ( y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) {\frac {1}{\sqrt {{\frac {1}{{a}^{2}} \left ( y \left ( x \right ) \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}+2\,{a}^{2}+2\,ax+ \left ( y \left ( x \right ) \right ) ^{2} \right ) }}}}}+x-{\frac {\sqrt {2}}{2} \left ( y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) {\it Arcsinh} \left ( {\frac {1}{2\,a} \left ( y \left ( x \right ) +\sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}} \right ) } \right ) {\frac {1}{\sqrt {{\frac {1}{{a}^{2}} \left ( y \left ( x \right ) \sqrt {4\,ax+ \left ( y \left ( x \right ) \right ) ^{2}}+2\,{a}^{2}+2\,ax+ \left ( y \left ( x \right ) \right ) ^{2} \right ) }}}}}=0 \right \} \]