ODE
\[ x y(x) y''(x)+x y'(x)^2+2 y(x) y'(x)=0 \] ODE Classification
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0446592 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {c_2 \sqrt {2-c_1 x}}{\sqrt {x}}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 18
\[ \left \{ {\frac { \left ( y \left ( x \right ) \right ) ^{2}}{2}}+{\frac {{\it \_C1}}{x}}-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[2*y[x]*y'[x] + x*y'[x]^2 + x*y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (Sqrt[2 - x*C[1]]*C[2])/Sqrt[x]}}
Maple raw input
dsolve(x*y(x)*diff(diff(y(x),x),x)+x*diff(y(x),x)^2+2*y(x)*diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
1/2*y(x)^2+_C1/x-_C2 = 0