y^{''}+6y^'-216y=0

Lösung

y^{^{''}} + 6 y^{^{'}} - 216 y = 0

y = c_{1} e^{12 t} + c_{2} e^{- 18 t}

Schritte zur Lösung

y^{''} (t) + 6 y^{'} (t) - 216 y = 0

Solve linear ODE:

y = c_{1} e^{12 t} + c_{2} e^{- 18 t}

y = c_{1} e^{12 t} + c_{2} e^{- 18 t}

y^{^{''}} + 6 y^{^{'}} + 16 y = 0

5 y^{^{''}} + 20 y = 0

(D^{4} - 2 D^{2} + 4) y = 0

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

(D^{3} - 2 D^{2} - D + 2) y = 0