\[ y''(x)-2 a y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.0590823 (sec), leaf count = 46
DSolve[-2*a*y[x]*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {\sqrt {c_1} \tan \left (\sqrt {a} \sqrt {c_1} x+\sqrt {a} \sqrt {c_1} c_2\right )}{\sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.893 (sec), leaf count = 23
dsolve(diff(diff(y(x),x),x)-2*a*y(x)*diff(y(x),x)=0,y(x))
\[y \left (x \right ) = \frac {\tan \left (\sqrt {c_{1} a}\, \left (x +c_{2}\right )\right ) \sqrt {c_{1} a}}{a}\]