y^{''}+9y^'+8y=0,y(0)=6,y^'(0)=-1

Lösung

y^{^{''}} + 9 y^{^{'}} + 8 y = 0, y (0) = 6, y^{^{'}} (0) = - 1

y = (6 + \frac{5}{7}) e^{- t} - \frac{5}{7} e^{- 8 t}

Schritte zur Lösung

y^{''} (t) + 9 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = (6 + \frac{5}{7}) e^{- t} - \frac{5}{7} e^{- 8 t}

y = (6 + \frac{5}{7}) e^{- t} - \frac{5}{7} e^{- 8 t}

y^{^{''''}} + 4 y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} - 12 y = 0

x^{^{'''}} + 3 x^{^{''}} + 3 x^{^{'}} + x = 0

y^{^{''}} - 2 y^{^{'}} - 8 y = 0, y (0) = a, y^{^{'}} (0) = - 8

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

2 y^{^{''}} + 12 y^{^{'}} + 24 y = 0, y (0) = 1, y^{^{'}} (0) = 4