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 = 0.0934945 (sec), leaf count = 19
\[\left \{\left \{y(x)\to c_2 x e^{\frac {c_1}{x}}+x\right \}\right \}\]
Maple ✓
cpu = 0.074 (sec), leaf count = 26
\[ \left \{ -\ln \left ( y \left ( x \right ) -x \right ) x+x\ln \left ( x \right ) + \left ( -{\it \_C1}-1 \right ) x+{\it \_C2}=0 \right \} \] 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),'implicit')
Maple raw output
-ln(y(x)-x)*x+x*ln(x)+(-_C1-1)*x+_C2 = 0