What is the solution for (dy)/(dt)+y= 1/(1+e^{2t)} ?

The solution for (dy)/(dt)+y= 1/(1+e^{2t)} is y=(arctan(e^t))/(e^t)+(c_{1})/(e^t)

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(dy)/(dt)+y= 1/(1+e^{2t)}

\frac{d y}{d t} + y = \frac{1}{1 + e ^{2 t}}

y = \frac{arctan ( e ^{t} )}{e ^{t}} + \frac{c _{1}}{e ^{t}}

Solution steps

\frac{d y}{d t} + y = \frac{1}{1 + e ^{2 t}}

Solve linear ODE:

y = \frac{arctan ( e ^{t} )}{e ^{t}} + \frac{c _{1}}{e ^{t}}

y = \frac{arctan ( e ^{t} )}{e ^{t}} + \frac{c _{1}}{e ^{t}}

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What is the solution for (dy)/(dt)+y= 1/(1+e^{2t)} ?
The solution for (dy)/(dt)+y= 1/(1+e^{2t)} is y=(arctan(e^t))/(e^t)+(c_{1})/(e^t)