y^{''}+2*y^'+y=e^{-t}

Lösung

y^{^{''}} + 2 \cdot y^{^{'}} + y = e^{- t}

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

Schritte zur Lösung

y^{''} (t) + 2 \cdot y^{'} (t) + y = e^{- t}

Solve linear ODE:

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

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

n = 0 \sum \infty \frac{1}{2 ^{n} n !}

d er i v a t i v e f (x) = \frac{( x ^{3} + 1 )}{( x ^{4} + 1 )}

x \to - 1 lim (\frac{x + 1}{x ^{2} - 1})

\int 2 4 - x^{2} d x

x \to π lim (\frac{( e ^{s i n (x)} - 1 )}{x - π})