y^{''}+2y^'+y=e^{-t}+9e^{5t}

Lösung

y^{^{''}} + 2 y^{^{'}} + y = e^{- t} + 9 e^{5 t}

y = c_{1} e^{- t} + c_{2} t e^{- t} + \frac{e ^{- t} t ^{2}}{2} + \frac{1}{4} e^{5 t}

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + y = e^{- t} + 9 e^{5 t}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} t e^{- t} + \frac{e ^{- t} t ^{2}}{2} + \frac{1}{4} e^{5 t}

y = c_{1} e^{- t} + c_{2} t e^{- t} + \frac{e ^{- t} t ^{2}}{2} + \frac{1}{4} e^{5 t}

n \to \infty lim (\frac{i}{n})

t a y l or (1 + z)^{\frac{1}{4}}

\frac{d}{d x} (5 x)

\frac{\partial}{\partial x} (y^{2} - cos (x) y)

\frac{d}{d x} (540 (1 - e^{- 0.1 x}))