What is the solution for y^'+y= 1/(1+e^{2x)} ?

The solution for y^'+y= 1/(1+e^{2x)} is y=(arctan(e^x))/(e^x)+(c_{1})/(e^x)

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y^'+y= 1/(1+e^{2x)}

y^{^{'}} + y = \frac{1}{1 + e ^{2 x}}

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

Solution steps

y^{'} (x) + y = \frac{1}{1 + e ^{2 x}}

Solve linear ODE:

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

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

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\frac{d}{d x} (2 x + 1)

f (x) = \frac{cos ( x )}{x ^{7}}

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\frac{d y}{d x} - 3 y = \frac{y}{x}

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