What is the solution for y^{''}+9y^'+14y=0,y(0)=0 ?

The solution for y^{''}+9y^'+14y=0,y(0)=0 is y=-c_{2}e^{-2t}+c_{2}e^{-7t}

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

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

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

Solution steps

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}

(\frac{d ^{2} y}{d x ^{2}}) + \frac{d y}{d x} - 6 y = 0

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

x^{^{''}} + 64 x = 0, x^{^{'}} = 0, x (0) = 0.5

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

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

What is the solution for y^{''}+9y^'+14y=0,y(0)=0 ?
The solution for y^{''}+9y^'+14y=0,y(0)=0 is y=-c_{2}e^{-2t}+c_{2}e^{-7t}