2.405 ODE No. 405
\[ a y'(x)^2+y(x) y'(x)-x=0 \]
✓ Mathematica : cpu = 0.71037 (sec), leaf count = 74
DSolve[-x + y[x]*Derivative[1][y][x] + a*Derivative[1][y][x]^2 == 0,y[x],x]
\[\text {Solve}\left [\left \{x=\frac {a K[1] \tan ^{-1}\left (\frac {K[1]}{\sqrt {1-K[1]^2}}\right )}{\sqrt {1-K[1]^2}}+\frac {c_1 K[1]}{\sqrt {1-K[1]^2}},y(x)=\frac {x}{K[1]}-a K[1]\right \},\{y(x),K[1]\}\right ]\]
✓ Maple : cpu = 0.323 (sec), leaf count = 378
dsolve(a*diff(y(x),x)^2+y(x)*diff(y(x),x)-x = 0,y(x))
\[\frac {c_{1} \left (y \left (x \right )-\sqrt {4 a x +y \left (x \right )^{2}}\right )}{\sqrt {\frac {-y \left (x \right )+\sqrt {4 a x +y \left (x \right )^{2}}+2 a}{a}}\, \sqrt {\frac {-y \left (x \right )+\sqrt {4 a x +y \left (x \right )^{2}}-2 a}{a}}}+x +\frac {\left (-y \left (x \right )+\sqrt {4 a x +y \left (x \right )^{2}}\right ) \ln \left (\frac {\sqrt {\frac {4 a x +2 y \left (x \right )^{2}-2 y \left (x \right ) \sqrt {4 a x +y \left (x \right )^{2}}-4 a^{2}}{a^{2}}}\, a +\sqrt {4 a x +y \left (x \right )^{2}}-y \left (x \right )}{2 a}\right )}{\sqrt {-\frac {2 \left (y \left (x \right ) \sqrt {4 a x +y \left (x \right )^{2}}+2 a^{2}-2 a x -y \left (x \right )^{2}\right )}{a^{2}}}} = 0\]