78.6.2 problem 2 (b)

Internal problem ID [18170]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 10 (Linear equations). Problems at page 82
Problem number : 2 (b)
Date solved : Tuesday, January 28, 2025 at 11:36:03 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y&=\frac {1}{1+{\mathrm e}^{2 x}} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 14

dsolve(diff(y(x),x)+y(x)=1/(1+exp(2*x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 18

DSolve[D[y[x],x]+y[x]==1/(1+Exp[2*x]),y[x],x,IncludeSingularSolutions -> True]
 

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