Internal problem ID [2624]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential
Equations. page 43
Problem number: Problem 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {{\mathrm e}^{y+x} y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(exp(x+y(x))*diff(y(x),x)-1=0,y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (c_{1} {\mathrm e}^{x}-1\right )-x \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 16
DSolve[Exp[x+y[x]]*y'[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \log \left (-e^{-x}+c_1\right ) \]