y^{''}+6y^'+9y=0,y(-1)=2,y^'(-1)=2

Lösung

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 2

y = 10 e^{- 3 t - 3} + 8 e^{- 3 t - 3} t

Schritte zur Lösung

y^{''} (t) + 6 y^{'} (t) + 9 y = 0

Solve linear ODE:

y = 10 e^{- 3 t - 3} + 8 e^{- 3 t - 3} t

y = 10 e^{- 3 t - 3} + 8 e^{- 3 t - 3} t

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = \frac{33}{4}

81 y^{^{''}} = - 16 y

y^{^{''}} + (0) y^{^{'}} + 36 y = 0, y (0) = 3, y^{^{'}} (0) = 0

y^{^{''}} - 14 y^{^{'}} + 74 y = 0, y (\frac{π}{10}) = 1, y (0) = 3

y^{^{''}} + 3 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = 9