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 = 0.321179 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {c_2 x}{\sqrt [3]{1+c_1 x^3}}\right \}\right \}\]
Maple ✓
cpu = 0.148 (sec), leaf count = 84
\[\left [y \left (x \right ) = \frac {x}{\left (-3 \textit {\_C2} \,x^{3}+\textit {\_C1} \right )^{\frac {1}{3}}}, y \left (x \right ) = \left (-\frac {1}{2 \left (-3 \textit {\_C2} \,x^{3}+\textit {\_C1} \right )^{\frac {1}{3}}}-\frac {i \sqrt {3}}{2 \left (-3 \textit {\_C2} \,x^{3}+\textit {\_C1} \right )^{\frac {1}{3}}}\right ) x, y \left (x \right ) = \left (-\frac {1}{2 \left (-3 \textit {\_C2} \,x^{3}+\textit {\_C1} \right )^{\frac {1}{3}}}+\frac {i \sqrt {3}}{2 \left (-3 \textit {\_C2} \,x^{3}+\textit {\_C1} \right )^{\frac {1}{3}}}\right ) x\right ]\] 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))
Maple raw output
[y(x) = 1/(-3*_C2*x^3+_C1)^(1/3)*x, y(x) = (-1/2/(-3*_C2*x^3+_C1)^(1/3)-1/2*I*3^(1/2)/(-3*_C2*x^3+_C1)^(1/3))*x, y(x) = (-1/2/(-3*_C2*x^3+_C1)^(1/3)+1/2*I*3^(1/2)/(-3*_C2*x^3+_C1)^(1/3))*x]