ODE
\[ x y(x) y''(x)+x y'(x)^2+y(x) y'(x)=0 \] 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 = 0.323007 (sec), leaf count = 19
\[\left \{\left \{y(x)\to c_2 \sqrt {2 \log (x)+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.172 (sec), leaf count = 31
\[\left [y \left (x \right ) = \sqrt {2 \ln \left (x \right ) \textit {\_C1} +2 \textit {\_C2}}, y \left (x \right ) = -\sqrt {2 \ln \left (x \right ) \textit {\_C1} +2 \textit {\_C2}}\right ]\] Mathematica raw input
DSolve[y[x]*y'[x] + x*y'[x]^2 + x*y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[2]*Sqrt[C[1] + 2*Log[x]]}}
Maple raw input
dsolve(x*y(x)*diff(diff(y(x),x),x)+x*diff(y(x),x)^2+y(x)*diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = (2*ln(x)*_C1+2*_C2)^(1/2), y(x) = -(2*ln(x)*_C1+2*_C2)^(1/2)]