Internal problem ID [5406]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+y-\frac {1}{1+{\mathrm e}^{2 x}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve(diff(y(x),x)+y(x)=1/(1+exp(2*x)),y(x), singsol=all)
\[ y \relax (x ) = \left (\arctan \left ({\mathrm e}^{x}\right )+c_{1}\right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 18
DSolve[y'[x]+y[x]==1/(1+Exp[2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (\text {ArcTan}\left (e^x\right )+c_1\right ) \\ \end{align*}