ODE No. 1812

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

✓ Mathematica : cpu = 0.299457 (sec), leaf count = 29

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

\[\left \{\left \{y(x)\to e^{\frac {c_1 x-1+c_2 c_1}{c_1 (x+c_2)}}\right \}\right \}\]

✓ Maple : cpu = 0.134 (sec), leaf count = 19

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))

\[y \left (x \right ) = {\mathrm e}^{\frac {x c_{1} +c_{2} -1}{x c_{1} +c_{2}}}\]