What is the solution for y^{''}+8y^'+97y=0,y(0)=9,y^'(0)=9 ?

The solution for y^{''}+8y^'+97y=0,y(0)=9,y^'(0)=9 is y=e^{-4t}(9cos(9t)+5sin(9t))

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y^{''}+8y^'+97y=0,y(0)=9,y^'(0)=9

y^{^{''}} + 8 y^{^{'}} + 97 y = 0, y (0) = 9, y^{^{'}} (0) = 9

y = e^{- 4 t} (9 cos (9 t) + 5 sin (9 t))

Solution steps

y^{''} (t) + 8 y^{'} (t) + 97 y = 0

Solve linear ODE:

y = e^{- 4 t} (9 cos (9 t) + 5 sin (9 t))

y = e^{- 4 t} (9 cos (9 t) + 5 sin (9 t))

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

\frac{1}{16} \frac{d ^{2} x}{d t ^{2}} = - 4 x

y^{^{''}} + 16 y = 0, y (\frac{π}{12}) = 2, y^{^{'}} (\frac{π}{12}) = - 4

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

y^{^{''}} + 3 y^{^{''}} + 3 y^{^{'}} + y = 0

What is the solution for y^{''}+8y^'+97y=0,y(0)=9,y^'(0)=9 ?
The solution for y^{''}+8y^'+97y=0,y(0)=9,y^'(0)=9 is y=e^{-4t}(9cos(9t)+5sin(9t))