1.3 problem 3

Internal problem ID [2037]

Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.4, page 36
Problem number: 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: 0.0 (sec). Leaf size: 15

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

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

Solution by Mathematica

Time used: 0.09 (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*}