ODE
\[ 2 x^2 y(x) y''(x)=x^2 y'(x)^2+2 x y(x) y'(x)-4 y(x)^2 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.41432 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_2 x^2 (\log (x)-2 c_1){}^2\right \}\right \}\]
Maple ✓
cpu = 0.048 (sec), leaf count = 32
\[\left [y \left (x \right ) = \frac {x^{2} \textit {\_C1}^{2}}{4 \textit {\_C2}}+\textit {\_C1} \,x^{2} \ln \left (x \right )+\textit {\_C2} \,x^{2} \ln \left (x \right )^{2}\right ]\] Mathematica raw input
DSolve[2*x^2*y[x]*y''[x] == -4*y[x]^2 + 2*x*y[x]*y'[x] + x^2*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> x^2*C[2]*(-2*C[1] + Log[x])^2}}
Maple raw input
dsolve(2*x^2*y(x)*diff(diff(y(x),x),x) = x^2*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)-4*y(x)^2, y(x))
Maple raw output
[y(x) = 1/4*x^2*_C1^2/_C2+_C1*x^2*ln(x)+_C2*x^2*ln(x)^2]