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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 5 y^{^{'}} + 10 y = 0

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

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

y^{^{''}} - 12 y^{^{'}} + 27 y = 0

y^{^{'''}} - 4 y^{^{''}} + 8 y^{^{'}} = 0