Internal problem ID [587]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{x +y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 13
dsolve(diff(y(x),x) = exp(x+y(x)),y(x), singsol=all)
\[ y \relax (x ) = \ln \left (-\frac {1}{{\mathrm e}^{x}+c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 0.329 (sec). Leaf size: 18
DSolve[y'[x] == Exp[x+y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\log \left (-e^x-c_1\right ) \\ \end{align*}