Internal problem ID [12320]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\ln \left (y-1\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)=ln(y(x)-1),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (\operatorname {Ei}_{1}\left (-\textit {\_Z} \right )+x +c_{1} \right )}+1 \]
✓ Solution by Mathematica
Time used: 0.29 (sec). Leaf size: 21
DSolve[y'[x]==Log[y[x]-1],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}[\operatorname {LogIntegral}(\text {$\#$1}-1)\&][x+c_1] y(x)\to 2 \end{align*}