ODE
\[ x^2 (x-y(x)) y''(x)+\left (x y'(x)-y(x)\right )^2=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.29123 (sec), leaf count = 19
\[\left \{\left \{y(x)\to x+c_2 x e^{\frac {c_1}{x}}\right \}\right \}\]
Maple ✓
cpu = 0.937 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {x \,{\mathrm e}^{\frac {\textit {\_C2}}{x}} {\mathrm e}^{-1}}{\textit {\_C1}}+x\right ]\] Mathematica raw input
DSolve[(-y[x] + x*y'[x])^2 + x^2*(x - y[x])*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x + E^(C[1]/x)*x*C[2]}}
Maple raw input
dsolve(x^2*(x-y(x))*diff(diff(y(x),x),x)+(x*diff(y(x),x)-y(x))^2 = 0, y(x))
Maple raw output
[y(x) = x/_C1*exp(_C2/x)*exp(-1)+x]