y^{'''}-2y^{''}-7y^'-4y=0

Lösung

y^{^{'''}} - 2 y^{^{''}} - 7 y^{^{'}} - 4 y = 0

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

Schritte zur Lösung

y^{'''} (t) - 2 y^{''} (t) - 7 y^{'} (t) - 4 y = 0

Solve linear ODE:

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

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

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 1

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

(d^{2} + 2 d + 1) y = 0

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

(d^{3} - 2 d^{2} - 3 d) y = 0