Internal problem ID [6159]
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]
\[ \boxed {y^{\prime }+y=\frac {1}{{\mathrm e}^{2 x}+1}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)+y(x)=1/(1+exp(2*x)),y(x), singsol=all)
\[ y \left (x \right ) = \left (\arctan \left ({\mathrm e}^{x}\right )+c_{1} \right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 18
DSolve[y'[x]+y[x]==1/(1+Exp[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (\arctan \left (e^x\right )+c_1\right ) \]