50.3.3 problem 1(c)

Internal problem ID [7827]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 1(c)
Date solved : Monday, January 27, 2025 at 03:24:21 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (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: 0.067 (sec). Leaf size: 18

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

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