\[ a y'(x)^2-y(x) y'(x)-x=0 \] ✓ Mathematica : cpu = 0.743245 (sec), leaf count = 57
DSolve[-x - y[x]*Derivative[1][y][x] + a*Derivative[1][y][x]^2 == 0,y[x],x]
\[\text {Solve}\left [\left \{x=\frac {a K[1] \sinh ^{-1}(K[1])}{\sqrt {K[1]^2+1}}+\frac {c_1 K[1]}{\sqrt {K[1]^2+1}},y(x)=a K[1]-\frac {x}{K[1]}\right \},\{y(x),K[1]\}\right ]\] ✓ Maple : cpu = 0.092 (sec), leaf count = 262
dsolve(a*diff(y(x),x)^2-y(x)*diff(y(x),x)-x = 0,y(x))
\[\frac {-\frac {\sqrt {2}\, \left (y \left (x \right )+\sqrt {4 a x +y \left (x \right )^{2}}\right ) \arcsinh \left (\frac {y \left (x \right )+\sqrt {4 a x +y \left (x \right )^{2}}}{2 a}\right )}{2}+x \sqrt {\frac {y \left (x \right ) \sqrt {4 a x +y \left (x \right )^{2}}+2 a^{2}+2 a x +y \left (x \right )^{2}}{a^{2}}}+c_{1} y \left (x \right )+c_{1} \sqrt {4 a x +y \left (x \right )^{2}}}{\sqrt {\frac {y \left (x \right ) \sqrt {4 a x +y \left (x \right )^{2}}+y \left (x \right )^{2}+2 a \left (x +a \right )}{a^{2}}}} = 0\]