19.1.3 problem 3

Internal problem ID [3517]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 3
Date solved : Monday, January 27, 2025 at 07:40:14 AM
CAS classification : [_separable]

\begin{align*} {\mathrm e}^{x +y} y^{\prime }-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 16

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

\[ y(x)\to \log \left (-e^{-x}+c_1\right ) \]