10.6.12 problem 12

Internal problem ID [1229]
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
Date solved : Monday, January 27, 2025 at 04:46:04 AM
CAS classification : [_linear]

\begin{align*} y+y^{\prime }&=\frac {1}{1+{\mathrm e}^{x}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(y(x)+diff(y(x),x) = 1/(1+exp(x)),y(x), singsol=all)
 

\[ y = \left (\ln \left (1+{\mathrm e}^{x}\right )+c_1 \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 20

DSolve[y[x]+D[y[x],x] == 1/(1+Exp[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\log \left (e^x+1\right )+c_1\right ) \]