ODE
\[ x y(x) y''(x)-2 x y'(x)^2+y(x) y'(x)=0 \] ODE Classification
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.044608 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \frac {c_2}{c_1-\log (x)}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 18
\[ \left \{ - \left ( y \left ( x \right ) \right ) ^{-1}-{\it \_C1}\,\ln \left ( x \right ) -{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[y[x]*y'[x] - 2*x*y'[x]^2 + x*y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[2]/(C[1] - Log[x])}}
Maple raw input
dsolve(x*y(x)*diff(diff(y(x),x),x)-2*x*diff(y(x),x)^2+y(x)*diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
-1/y(x)-_C1*ln(x)-_C2 = 0