y^{''''}+2y^{'''}+y^{''}=0

Lösung

y^{^{''''}} + 2 y^{^{'''}} + y^{^{''}} = 0

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

Schritte zur Lösung

y^{(4)} (t) + 2 y^{'''} (t) + y^{''} (t) = 0

Solve linear ODE:

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

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

y^{^{''''}} - 7 y^{^{'''}} - 49 y^{^{''}} + 343 y^{^{'}} = 0

y^{^{''}} + 18 y^{^{'}} + 82 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''''}} - 6 y^{^{'''}} + 13 y^{^{''}} - 12 y^{^{'}} + 4 y = 0

2 y^{^{'''}} - y^{^{''}} - y^{^{'}} = 0

7 y^{^{''}} - 56 y^{^{'}} + 112 y = 0