Internal problem ID [2115]
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]
Solve \begin {gather*} \boxed {{\mathrm e}^{x +y} y^{\prime }-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 15
dsolve(exp(x+y(x))*diff(y(x),x)-1=0,y(x), singsol=all)
\[ y \relax (x ) = \ln \left (c_{1} {\mathrm e}^{x}-1\right )-x \]
✓ Solution by Mathematica
Time used: 0.099 (sec). Leaf size: 15
DSolve[Exp[x+y[x]]*y'[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log (\sinh (x)-\cosh (x)+c_1) \\ \end{align*}