ODE
\[ x y(x) y''(x)=x y'(x)^2-y(x) y'(x) \] ODE Classification
[_Liouville, [_Painleve, `3rd`], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.198844 (sec), leaf count = 12
\[\left \{\left \{y(x)\to c_2 x^{c_1}\right \}\right \}\]
Maple ✓
cpu = 0.858 (sec), leaf count = 9
\[[y \left (x \right ) = x^{\textit {\_C1}} \textit {\_C2}]\] Mathematica raw input
DSolve[x*y[x]*y''[x] == -(y[x]*y'[x]) + x*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> x^C[1]*C[2]}}
Maple raw input
dsolve(x*y(x)*diff(diff(y(x),x),x) = x*diff(y(x),x)^2-y(x)*diff(y(x),x), y(x))
Maple raw output
[y(x) = x^_C1*_C2]