Internal problem ID [9197]
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')`]
\[ \boxed {y^{\prime }+\left (\frac {\operatorname {expIntegral}_{1}\left (-\ln \left (y-1\right )\right )}{x}-f_{1} \left (x \right )\right ) \ln \left (y-1\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (\left (\int \frac {f_{1} \left (x \right )}{x}d x \right ) x +x c_{1} +\operatorname {Ei}_{1}\left (-\textit {\_Z} \right )\right )}+1 \]
✗ 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