Internal problem ID [579]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y+y^{\prime }-\frac {1}{{\mathrm e}^{x}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 16
dsolve(y(x)+diff(y(x),x) = 1/(1+exp(x)),y(x), singsol=all)
\[ y \relax (x ) = \left (\ln \left (1+{\mathrm e}^{x}\right )+c_{1}\right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 20
DSolve[y[x]+y'[x] == 1/(1+Exp[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (\log \left (e^x+1\right )+c_1\right ) \\ \end{align*}