y^'+y= 1/(1+e^x)

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

\int_{0}^{t} 5 e^{s} sin (t - s) d s

\int \frac{cos ( x )}{( sin ^{2} ( x ) ) ^{\frac{1}{3}}} d x

x \to 0 lim (\frac{sin ( 14 x )}{x})

\int sin (e^{x}) d x

d er i v a t i v e f (x) = 8 (2 x - 3)^{3}