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 = 0.101989 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \sqrt {2} \sqrt {c_1} \tanh \left (\frac {\sqrt {c_1} \left (c_2+x\right )}{\sqrt {2}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.07 (sec), leaf count = 24
\[ \left \{ \sqrt {2}{\it \_C1}\,{\it Artanh} \left ( {\frac {y \left ( x \right ) \sqrt {2}{\it \_C1}}{2}} \right ) -x-{\it \_C2}=0 \right \} \] 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),'implicit')
Maple raw output
2^(1/2)*_C1*arctanh(1/2*y(x)*2^(1/2)*_C1)-x-_C2 = 0