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 = 0.552954 (sec), leaf count = 53
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\exp \left (-\int _1^{K[2]}\frac {\log (K[1])+1}{K[1] (\log (K[1])-1)}dK[1]\right )}{c_1}dK[2]\& \right ][x+c_2]\right \}\right \}\]
Maple ✓
cpu = 1.276 (sec), leaf count = 19
\[\left [y \left (x \right ) = {\mathrm e}^{\frac {\textit {\_C1} x +\textit {\_C2} -1}{\textit {\_C1} x +\textit {\_C2}}}\right ]\] 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
{{y[x] -> InverseFunction[Inactive[Integrate][1/(E^Inactive[Integrate][(1 + log[K[1]])/(K[1]*(-1 + Log[K[1]])), {K[1], 1, K[2]}]*C[1]), {K[2], 1, #1}] & ][x + C[2]]}}
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))
Maple raw output
[y(x) = exp((_C1*x+_C2-1)/(_C1*x+_C2))]