15.1.26 problem 26

Internal problem ID [2866]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 26
Date solved : Monday, January 27, 2025 at 06:20:47 AM
CAS classification : [_quadrature]

\begin{align*} {\mathrm e}^{y} \left (y^{\prime }+1\right )&=1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 1.654 (sec). Leaf size: 22

dsolve([exp(y(x))*(diff(y(x),x)+1)=1,y(0) = 1],y(x), singsol=all)
 

\[ y = -x +\ln \left (-{\mathrm e}^{x}-{\mathrm e}+1\right )-i \pi \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 18

DSolve[{Exp[y[x]]*(D[y[x],x]+1)==1,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \log \left (e^{-x} \left (e^x-1+e\right )\right ) \]