ODE
\[ y''(x)+y(x) y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.219373 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \sqrt {2} \sqrt {c_1} \tanh \left (\frac {\sqrt {c_1} (x+c_2)}{\sqrt {2}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.401 (sec), leaf count = 23
\[\left [y \left (x \right ) = \frac {\tanh \left (\frac {\left (x +\textit {\_C2} \right ) \sqrt {2}}{2 \textit {\_C1}}\right ) \sqrt {2}}{\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[y[x]*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[2]*Sqrt[C[1]]*Tanh[(Sqrt[C[1]]*(x + C[2]))/Sqrt[2]]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+y(x)*diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = tanh(1/2*(x+_C2)*2^(1/2)/_C1)*2^(1/2)/_C1]