y^{'''}-3y^{''}-9y^'-5y=0

Lösung

y^{^{'''}} - 3 y^{^{''}} - 9 y^{^{'}} - 5 y = 0

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

Schritte zur Lösung

y^{'''} (t) - 3 y^{''} (t) - 9 y^{'} (t) - 5 y = 0

Solve linear ODE:

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

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

3 y^{^{''}} - 16 y^{^{'}} + 13 y = 0

y^{^{''}} + n^{2} y = 0, y (0) = c, y^{^{'}} (0) = v

4 y^{^{''}} - 8 y^{^{'}} + 3 y = 0, y (0) = 2, y^{^{'}} (0) = \frac{1}{2}

f^{^{''}} (t) - f^{^{'}} (t) - 2 f (t) = 0, f (0) = 1, f^{^{'}} (0) = 0

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 1