4.2 problem 2(b)

Internal problem ID [2600]

Book: Differential equations with applications and historial notes, George F. Simmons, 1971
Section: Chapter 2, section 11, page 49
Problem number: 2(b).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }+y-\frac {1}{{\mathrm e}^{2 x}+1}=0} \end {gather*}

Solution by Maple

Time used: 0.002 (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: 0.086 (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*}