x^{''}+4x^'+4x=e^{-2t}

Lösung

x^{^{''}} + 4 x^{^{'}} + 4 x = e^{- 2 t}

x = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{e ^{- 2 t} t ^{2}}{2}

Schritte zur Lösung

x^{''} (t) + 4 x^{'} (t) + 4 x = e^{- 2 t}

Solve linear ODE:

x = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{e ^{- 2 t} t ^{2}}{2}

x = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{e ^{- 2 t} t ^{2}}{2}

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

\int_{0}^{8} - x^{2} + 2 x + 4 d x

t an g e n t f (x) = \frac{4 x}{x + 1}, at x = 3

x \to - 4 lim (\frac{∣ x + 4 ∣}{x + 4})

d er i v a t i v e y = (e^{4 x} - 3)^{8}