ODE
\[ x^2 y(x)^2 y''(x)=\left (x^2+y(x)^2\right ) \left (x y'(x)-y(x)\right ) \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 1.06308 (sec), leaf count = 35
\[\left \{\left \{y(x)\to -\frac {x \left (1+W\left (-e^{-1-c_2 c_1{}^2} x^{c_1{}^2}\right )\right )}{c_1}\right \}\right \}\]
Maple ✓
cpu = 1.225 (sec), leaf count = 28
\[\left [y \left (x \right ) = -\frac {x \left (\LambertW \left (-x^{\textit {\_C1}^{2}} {\mathrm e}^{\textit {\_C1}^{2} \textit {\_C2}} {\mathrm e}^{-1}\right )+1\right )}{\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[x^2*y[x]^2*y''[x] == (x^2 + y[x]^2)*(-y[x] + x*y'[x]),y[x],x]
Mathematica raw output
{{y[x] -> -((x*(1 + ProductLog[-(E^(-1 - C[1]^2*C[2])*x^C[1]^2)]))/C[1])}}
Maple raw input
dsolve(x^2*y(x)^2*diff(diff(y(x),x),x) = (x^2+y(x)^2)*(x*diff(y(x),x)-y(x)), y(x))
Maple raw output
[y(x) = -x*(LambertW(-x^(_C1^2)*exp(_C1^2*_C2)*exp(-1))+1)/_C1]