y^{''}+18y^'+80y=0,y(0)=9,y^'(0)=-76

Lösung

y^{^{''}} + 18 y^{^{'}} + 80 y = 0, y (0) = 9, y^{^{'}} (0) = - 76

y = 7 e^{- 8 t} + 2 e^{- 10 t}

Schritte zur Lösung

y^{''} (t) + 18 y^{'} (t) + 80 y = 0

Solve linear ODE:

y = 7 e^{- 8 t} + 2 e^{- 10 t}

y = 7 e^{- 8 t} + 2 e^{- 10 t}

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

(d - 5 d^{2} + 4 d - 20) x = 0

25 x^{^{''}} + 50 x^{^{'}} + 169 x = 0

45 y^{^{''}} + 180 y = 0

\frac{1}{8} x^{^{''}} + 25 x = 0