y^{'''}+3y^{''}-7y^'+3y=0

Lösung

y^{^{'''}} + 3 y^{^{''}} - 7 y^{^{'}} + 3 y = 0

y = c_{1} e^{t} + c_{2} e^{(- 2 + 7) t} + c_{3} e^{(- 2 - 7) t}

Schritte zur Lösung

y^{'''} (t) + 3 y^{''} (t) - 7 y^{'} (t) + 3 y = 0

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{(- 2 + 7) t} + c_{3} e^{(- 2 - 7) t}

y = c_{1} e^{t} + c_{2} e^{(- 2 + 7) t} + c_{3} e^{(- 2 - 7) t}

y^{^{''}} + 6 y^{^{'}} + 16 y = 0, y (0) = 4, y^{^{'}} (0) = 0

5 y^{^{''}} - 30 y^{^{'}} + 170 y = 0

y^{^{''}} + 14 y^{^{'}} + 49 y = 0, y (- 4) = 1, y^{^{'}} (- 4) = 5

y^{^{'''}} - 49 y^{^{'}} = 0

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = e^{- \frac{π}{6}}