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 = 0.044136 (sec), leaf count = 18
\[\left \{\left \{y(x)\to \frac {c_2}{x^2-2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 18
\[ \left \{ {\it \_C1}\,{x}^{2}-{\it \_C2}- \left ( y \left ( x \right ) \right ) ^{-1}=0 \right \} \] 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]/(x^2 - 2*C[1])}}
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
_C1*x^2-_C2-1/y(x) = 0