What is the solution for y^{''}+14y^'+48y=0,y(0)=9,y^'(0)=-66 ?

The solution for y^{''}+14y^'+48y=0,y(0)=9,y^'(0)=-66 is y=3e^{-6t}+6e^{-8t}

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y^{''}+14y^'+48y=0,y(0)=9,y^'(0)=-66

y^{^{''}} + 14 y^{^{'}} + 48 y = 0, y (0) = 9, y^{^{'}} (0) = - 66

y = 3 e^{- 6 t} + 6 e^{- 8 t}

Solution steps

y^{''} (t) + 14 y^{'} (t) + 48 y = 0

Solve linear ODE:

y = 3 e^{- 6 t} + 6 e^{- 8 t}

y = 3 e^{- 6 t} + 6 e^{- 8 t}

y^{^{''''}} = 625 y

2 y^{^{''}} + 8 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} + 4 y + 5 y = 0

\frac{d ^{2} y}{d x ^{2}} + 10 \frac{d y}{d x} + 41 y = 0

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

What is the solution for y^{''}+14y^'+48y=0,y(0)=9,y^'(0)=-66 ?
The solution for y^{''}+14y^'+48y=0,y(0)=9,y^'(0)=-66 is y=3e^{-6t}+6e^{-8t}