y^{''''}+4y^{'''}-y^{''}-16y^'-12y=0

Lösung

y^{^{''''}} + 4 y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} - 12 y = 0

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + c_{3} e^{- 2 t} + c_{4} e^{2 t}

Schritte zur Lösung

y^{(4)} (t) + 4 y^{'''} (t) - y^{''} (t) - 16 y^{'} (t) - 12 y = 0

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + c_{3} e^{- 2 t} + c_{4} e^{2 t}

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + c_{3} e^{- 2 t} + c_{4} e^{2 t}

x^{^{'''}} + 3 x^{^{''}} + 3 x^{^{'}} + x = 0

y^{^{''}} - 2 y^{^{'}} - 8 y = 0, y (0) = a, y^{^{'}} (0) = - 8

y^{^{''}} + 3 y^{^{'}} = 0, y^{^{'}} (0) = 0, y (0) = 0

2 y^{^{''}} + 12 y^{^{'}} + 24 y = 0, y (0) = 1, y^{^{'}} (0) = 4

4 y^{^{''}} - 4 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = - 1