Internal problem ID [8442]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 862.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }+\left (\frac {\expIntegral \left (1, -\ln \left (-1+y\right )\right )}{x}-\textit {\_F1} \relax (x )\right ) \ln \left (-1+y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(diff(y(x),x) = -(1/x*Ei(1,-ln(-1+y(x)))-_F1(x))*ln(-1+y(x)),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (\left (\int \frac {\textit {\_F1} \relax (x )}{x}d x \right ) x +x c_{1}+\expIntegral \left (1, -\textit {\_Z} \right )\right )}+1 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x] == (-(ExpIntegralEi[-Log[-1 + y[x]]]/x) + F1[x])*Log[-1 + y[x]],y[x],x,IncludeSingularSolutions -> True]
Not solved