ODE
\[ a y(x) y'(x)+x y(x) y''(x)+2 x y'(x)^2=0 \] 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 = 0.146685 (sec), leaf count = 33
\[\left \{\left \{y(x)\to c_2 x^{-a/3} \sqrt [3]{3 x-(a-1) c_1 x^a}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 21
\[ \left \{ {\frac {{\it \_C1}\,x}{{x}^{a}}}-{\it \_C2}+{\frac { \left ( y \left ( x \right ) \right ) ^{3}}{3}}=0 \right \} \] Mathematica raw input
DSolve[a*y[x]*y'[x] + 2*x*y'[x]^2 + x*y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((3*x - (-1 + a)*x^a*C[1])^(1/3)*C[2])/x^(a/3)}}
Maple raw input
dsolve(x*y(x)*diff(diff(y(x),x),x)+2*x*diff(y(x),x)^2+a*y(x)*diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
_C1*x/(x^a)-_C2+1/3*y(x)^3 = 0