y^{''}+9y^'+14y=0,y(0)=0

Lösung

y^{^{''}} + 9 y^{^{'}} + 14 y = 0, y (0) = 0

y = - c_{2} e^{- 2 t} + c_{2} e^{- 7 t}

Schritte zur Lösung

y^{''} (t) + 9 y^{'} (t) + 14 y = 0

Solve linear ODE:

y = - c_{2} e^{- 2 t} + c_{2} e^{- 7 t}

y = - c_{2} e^{- 2 t} + c_{2} e^{- 7 t}

x^{^{''}} + 2 ab x^{^{'}} + b^{2} x = 0

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

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

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

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