y^{''}+4y^'+4y=0,y(0)=-2,y^'(0)=9

Lösung

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = - 2, y^{^{'}} (0) = 9

y = - 2 e^{- 2 t} + 5 e^{- 2 t} t

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = - 2 e^{- 2 t} + 5 e^{- 2 t} t

y = - 2 e^{- 2 t} + 5 e^{- 2 t} t

x^{^{''}} + 0.5 \cdot x^{^{'}} + \frac{17}{16} \cdot x = 0

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 4

y^{^{''}} + 4 y^{^{'}} + 7 y = 0, y (0) = 1, y^{^{'}} (0) = - 2

y^{^{''}} - 7 y^{^{'}} - 8 y = 0, y (0) = 2, y^{^{'}} (0) = 7

y^{^{''}} - y^{^{'}} = - y