26.4.2 problem 2(b)

Internal problem ID [4270]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 11, page 49
Problem number : 2(b)
Date solved : Monday, January 27, 2025 at 08:47:12 AM
CAS classification : [_linear]

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

✓ 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)
 

\[ y \left (x \right ) = \left (\arctan \left ({\mathrm e}^{x}\right )+c_{1} \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 18

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

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