ODE
\[ x y(x) y''(x)-4 x y'(x)^2+4 y(x) y'(x)=0 \] 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 = 0.0534294 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {c_2 x}{\sqrt [3]{c_1 x^3+1}}\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 18
\[ \left \{ {\frac {{\it \_C1}}{{x}^{3}}}-{\it \_C2}-{\frac {1}{3\, \left ( y \left ( x \right ) \right ) ^{3}}}=0 \right \} \] Mathematica raw input
DSolve[4*y[x]*y'[x] - 4*x*y'[x]^2 + x*y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x*C[2])/(1 + x^3*C[1])^(1/3)}}
Maple raw input
dsolve(x*y(x)*diff(diff(y(x),x),x)-4*x*diff(y(x),x)^2+4*y(x)*diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
_C1/x^3-_C2-1/3/y(x)^3 = 0