y^{'''}+10y^{''}-y^'-3y=0

Lösung

y^{^{'''}} + 10 y^{^{''}} - y^{^{'}} - 3 y = 0

y = c_{1} e^{- 0.51207 \dots t} + c_{2} e^{0.58179 \dots t} + c_{3} e^{- 10.06972 \dots t}

Schritte zur Lösung

y^{'''} (t) + 10 y^{''} (t) - y^{'} (t) - 3 y = 0

Solve linear ODE:

y = c_{1} e^{- 0.51207 \dots t} + c_{2} e^{0.58179 \dots t} + c_{3} e^{- 10.06972 \dots t}

y = c_{1} e^{- 0.51207 \dots t} + c_{2} e^{0.58179 \dots t} + c_{3} e^{- 10.06972 \dots t}

y^{^{''}} + 9 y = 0, y (0) = 3, y^{^{'}} (0) = 12

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

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} - 6 y^{^{'}} + 5 y = 0, y^{0} = 3

y^{^{''}} + 2 y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = - 2