4.41.46 \(y(x) y''(x) (1-\log (y(x)))+y'(x)^2 (\log (y(x))+1)=0\)

ODE
\[ y(x) y''(x) (1-\log (y(x)))+y'(x)^2 (\log (y(x))+1)=0 \] ODE Classification

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Book solution method
TO DO

Mathematica
cpu = 599.998 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 0.059 (sec), leaf count = 20

\[ \left \{ - \left ( -1+\ln \left ( y \left ( x \right ) \right ) \right ) ^{-1}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \] Mathematica raw input

DSolve[(1 + log[y[x]])*y'[x]^2 + (1 - Log[y[x]])*y[x]*y''[x] == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(y(x)*(1-ln(y(x)))*diff(diff(y(x),x),x)+(1+ln(y(x)))*diff(y(x),x)^2 = 0, y(x),'implicit')

Maple raw output

-1/(-1+ln(y(x)))-_C1*x-_C2 = 0