Internal problem ID [582]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left ({\mathrm e}^{x}+1\right ) y^{\prime }-y+{\mathrm e}^{x} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve((1+exp(x))*diff(y(x),x) = y(x)-exp(x)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{x}}{\left (1+{\mathrm e}^{x}\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 23
DSolve[(1+Exp[x])*y'[x]== y[x]-Exp[x]*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 e^x}{\left (e^x+1\right )^2} \\ y(x)\to 0 \\ \end{align*}