2.862   ODE No. 862

\[ y'(x)=\log (y(x)-1) \left (\text {$\_$F1}(x)-\frac {\text {Ei}(-\log (y(x)-1))}{x}\right ) \]

✗ Mathematica : cpu = 0.494515 (sec), leaf count = 0

DSolve[Derivative[1][y][x] == Log[-1 + y[x]]*(-(ExpIntegralEi[-Log[-1 + y[x]]]/x) + _F1[x]),y[x],x]
 

, could not solve

DSolve[Derivative[1][y][x] == Log[-1 + y[x]]*(-(ExpIntegralEi[-Log[-1 + y[x]]]/x) + _F1[x]), y[x], x]

✓ Maple : cpu = 0.164 (sec), leaf count = 27

dsolve(diff(y(x),x) = -(1/x*Ei(1,-ln(-1+y(x)))-_F1(x))*ln(-1+y(x)),y(x))
 

\[y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (\left (\int \frac {\textit {\_F1} \left (x \right )}{x}d x \right ) x +x c_{1} +\operatorname {Ei}_{1}\left (-\textit {\_Z} \right )\right )}+1\]