3y^{'''}+9y^{''}+y^'-8y=e^{-t}

Lösung

3 y^{^{'''}} + 9 y^{^{''}} + y^{^{'}} - 8 y = e^{- t}

y = c_{1} e^{0.79544 \dots t} + c_{2} e^{- 1.39878 \dots t} + c_{3} e^{- 2.39666 \dots t} - \frac{1}{3} e^{- t}

Schritte zur Lösung

3 y^{'''} (t) + 9 y^{''} (t) + y^{'} (t) - 8 y = e^{- t}

Solve linear ODE:

y = c_{1} e^{0.79544 \dots t} + c_{2} e^{- 1.39878 \dots t} + c_{3} e^{- 2.39666 \dots t} - \frac{1}{3} e^{- t}

y = c_{1} e^{0.79544 \dots t} + c_{2} e^{- 1.39878 \dots t} + c_{3} e^{- 2.39666 \dots t} - \frac{1}{3} e^{- t}

y^{^{''}} + y = (t - u), y (0) = 10, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 13 y = cos (3 x) - sin (3 x)

- x^{^{''}} - 3 x^{^{'}} - 2 = t

y^{^{''}} - y = - 4 t + 3

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