ODE
\[ \left (x^2 y(x) y''(x)+x^2 \left (-y'(x)^2\right )+y(x)^2\right )^2=4 x y(x) \left (x y'(x)-y(x)\right )^3 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 20.4514 (sec), leaf count = 19
\[\left \{\left \{y(x)\to c_1 x e^{\frac {1}{-x+c_2}}\right \}\right \}\]
Maple ✓
cpu = 1.809 (sec), leaf count = 11
\[[y \left (x \right ) = \textit {\_C1} x, y \left (x \right ) = 0]\] Mathematica raw input
DSolve[(y[x]^2 - x^2*y'[x]^2 + x^2*y[x]*y''[x])^2 == 4*x*y[x]*(-y[x] + x*y'[x])^3,y[x],x]
Mathematica raw output
{{y[x] -> E^(-x + C[2])^(-1)*x*C[1]}}
Maple raw input
dsolve((y(x)^2-x^2*diff(y(x),x)^2+x^2*y(x)*diff(diff(y(x),x),x))^2 = 4*x*y(x)*(x*diff(y(x),x)-y(x))^3, y(x))
Maple raw output
[y(x) = _C1*x, y(x) = 0]