y^{'''}-2y^{''}-9y^'+18y=0

Lösung

y^{^{'''}} - 2 y^{^{''}} - 9 y^{^{'}} + 18 y = 0

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

Schritte zur Lösung

y^{'''} (t) - 2 y^{''} (t) - 9 y^{'} (t) + 18 y = 0

Solve linear ODE:

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

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

4 y^{^{''}} - 4 y^{^{'}} - 3 y = 0, y (0) = 5

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = 8, y^{^{'}} (0) = - 14

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 25 y = 0, y (0) = 1, y^{^{'}} (0) = 5

y^{^{''}} + 6 y^{^{'}} + 34 y = 0, y (0) = 2, y^{^{'}} (0) = - 5