What is the solution for y^{''}+12y^'+27y=0,y(0)=11,y^'(0)=-81 ?

The solution for y^{''}+12y^'+27y=0,y(0)=11,y^'(0)=-81 is y=3e^{-3t}+8e^{-9t}

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y^{''}+12y^'+27y=0,y(0)=11,y^'(0)=-81

y^{^{''}} + 12 y^{^{'}} + 27 y = 0, y (0) = 11, y^{^{'}} (0) = - 81

y = 3 e^{- 3 t} + 8 e^{- 9 t}

Solution steps

y^{''} (t) + 12 y^{'} (t) + 27 y = 0

Solve linear ODE:

y = 3 e^{- 3 t} + 8 e^{- 9 t}

y = 3 e^{- 3 t} + 8 e^{- 9 t}

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

4 y^{^{''}} - 4 y - 3 y = 0

\frac{d ^{2} x}{d t ^{2}} + 10 \frac{d x}{d t} + 25 x = 0

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 9, y^{^{'}} (0) = - 60

y^{^{'''}} - 7 y^{^{''}} + 12 y^{^{'}} = 0

What is the solution for y^{''}+12y^'+27y=0,y(0)=11,y^'(0)=-81 ?
The solution for y^{''}+12y^'+27y=0,y(0)=11,y^'(0)=-81 is y=3e^{-3t}+8e^{-9t}