y^{'''}-5y^{''}+2y^'+8y=0

Lösung

y^{^{'''}} - 5 y^{^{''}} + 2 y^{^{'}} + 8 y = 0

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

Schritte zur Lösung

y^{'''} (t) - 5 y^{''} (t) + 2 y^{'} (t) + 8 y = 0

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} - 3 y = 0

y^{^{''}} + 9 y^{^{'}} + 8 y = 0

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

4 y^{^{''}} + 4 y^{^{'}} + 3 y = 0

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