71.4.4 problem 4

Internal problem ID [14376]
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
Date solved : Tuesday, January 28, 2025 at 06:28:12 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\ln \left (y-1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

dsolve(diff(y(x),x)=ln(y(x)-1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.181 (sec). Leaf size: 31

DSolve[D[y[x],x]==Log[y[x]-1],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\log (K[1]-1)}dK[1]\&\right ][x+c_1] \\ y(x)\to 2 \\ \end{align*}