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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

(4 D^{4} + 20 D^{3} + 35 D^{2} + 25 D + 6) y = 0

(D^{2} - 4 D + 4) y = 0

25 x^{^{''}} - 20 x^{^{'}} + 4 x = 0

\frac{d ^{2} y}{d x ^{2}} = - k y

2 y^{^{''}} + 5 y^{^{'}} + 2 y = 0