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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

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

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = - 7

2 y^{^{''}} + 2 y^{^{'}} + 3 y = 0

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 15, y^{^{'}} (0) = - 6