y^{''}+2y^'+y=3sqrt((t-1))e^{-1}

Lösung

y^{^{''}} + 2 y^{^{'}} + y = 3 (t - 1) e^{- 1}

y = c_{1} e^{- t} + c_{2} t e^{- t} + e^{- t} \cdot \int - 3 e^{t - 1} t t - 1 d t + 6 e^{- t} t (\frac{1}{2} e^{t - 1} t - 1 - \frac{π}{4} erfi (t - 1))

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + y = 3 (t - 1) e^{- 1}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} t e^{- t} + e^{- t} \cdot \int - 3 e^{t - 1} t t - 1 d t + 6 e^{- t} t (\frac{1}{2} e^{t - 1} t - 1 - \frac{π}{4} erfi (t - 1))

y = c_{1} e^{- t} + c_{2} t e^{- t} + e^{- t} \cdot \int - 3 e^{t - 1} t t - 1 d t + 6 e^{- t} t (\frac{1}{2} e^{t - 1} t - 1 - \frac{π}{4} erfi (t - 1))

y^{^{'''}} + y^{^{''}} = x + 1

y^{^{''}} + y - 20 y = (x + 1) e^{x}

y^{^{''}} - 4 y = sin (2 x)

y^{^{''}} + 5 y^{^{'}} + 4 x = 0

y^{^{''}} + 25 y = 25, y (0) = 1, y^{^{'}} (0) = - 5