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Beliebt Rechnen >

(dy)/(dx)+y=(1-e^{-2x})/(e^x+e^{-x)}

Lösung

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

Lösung

y = \frac{ln ( e ^{2 x} + 1 )}{e ^{x}} - \frac{x}{e ^{x}} + \frac{c _{1}}{e ^{x}}

Schritte zur Lösung

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

Solve linear ODE:

y = \frac{ln ( e ^{2 x} + 1 )}{e ^{x}} - \frac{x}{e ^{x}} + \frac{c _{1}}{e ^{x}}

y = \frac{ln ( e ^{2 x} + 1 )}{e ^{x}} - \frac{x}{e ^{x}} + \frac{c _{1}}{e ^{x}}

Graph

Beliebte Beispiele

derivative of x^{-4}+cos(x)

\frac{d}{d x} (x^{- 4} + cos (x))

f(x)=(cos(t))/(t^7)

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

limit as x approaches-3 of 2x+1

x \to - 3 lim (2 x + 1)

integral of 1/(x^2+6x+10)

\int \frac{1}{x ^{2} + 6 x + 10} d x

limit as x approaches 2 of x(x+1)(x+2)

x \to 2 lim (x (x + 1) (x + 2))