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]
\[ \boxed {y+y^{\prime }-\frac {1}{{\mathrm e}^{2 x}+1}=0} \]
✓ 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: 0.08 (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 (\arctan \left (e^x\right )+c_1\right ) \\ \end{align*}