y^{'''}+4y^{''}-7y^'-10y=0

Lösung

y^{^{'''}} + 4 y^{^{''}} - 7 y^{^{'}} - 10 y = 0

y = c_{1} e^{- t} + c_{2} e^{2 t} + c_{3} e^{- 5 t}

Schritte zur Lösung

y^{'''} (t) + 4 y^{''} (t) - 7 y^{'} (t) - 10 y = 0

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{2 t} + c_{3} e^{- 5 t}

y = c_{1} e^{- t} + c_{2} e^{2 t} + c_{3} e^{- 5 t}

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = 5, y^{^{'}} (0) = 0

(y^{^{''''}} + 8 y^{^{''}} + 16 y)^{2} = 0

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 0