ODE
\[ x y(x) y''(x)+2 x y'(x)^2+y(x) y'(x)=0 \] ODE Classification
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.332138 (sec), leaf count = 19
\[\left \{\left \{y(x)\to c_2 \sqrt [3]{3 \log (x)+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.17 (sec), leaf count = 83
\[\left [y \left (x \right ) = \left (3 \ln \left (x \right ) \textit {\_C1} +3 \textit {\_C2} \right )^{\frac {1}{3}}, y \left (x \right ) = -\frac {\left (3 \ln \left (x \right ) \textit {\_C1} +3 \textit {\_C2} \right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (3 \ln \left (x \right ) \textit {\_C1} +3 \textit {\_C2} \right )^{\frac {1}{3}}}{2}, y \left (x \right ) = -\frac {\left (3 \ln \left (x \right ) \textit {\_C1} +3 \textit {\_C2} \right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (3 \ln \left (x \right ) \textit {\_C1} +3 \textit {\_C2} \right )^{\frac {1}{3}}}{2}\right ]\] Mathematica raw input
DSolve[y[x]*y'[x] + 2*x*y'[x]^2 + x*y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[2]*(C[1] + 3*Log[x])^(1/3)}}
Maple raw input
dsolve(x*y(x)*diff(diff(y(x),x),x)+2*x*diff(y(x),x)^2+y(x)*diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = (3*ln(x)*_C1+3*_C2)^(1/3), y(x) = -1/2*(3*ln(x)*_C1+3*_C2)^(1/3)-1/2*I*3^(1/2)*(3*ln(x)*_C1+3*_C2)^(1/3), y(x) = -1/2*(3*ln(x)*_C1+3*_C2)^(1/3)+1/2*I*3^(1/2)*(3*ln(x)*_C1+3*_C2)^(1/3)]