What is the solution for y^{''}+18y^'+82y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+18y^'+82y=0,y(0)=1,y^'(0)=0 is y=e^{-9t}(cos(t)+9sin(t))

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y^{''}+18y^'+82y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 18 y^{^{'}} + 82 y = 0, y (0) = 1, y^{^{'}} (0) = 0

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

Solution steps

y^{''} (t) + 18 y^{'} (t) + 82 y = 0

Solve linear ODE:

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

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

2 x^{^{''}} + 8 x^{^{'}} + 10 x = 0

0.2 q^{^{''}} + 5 q^{^{'}} + 500 q = 0

x^{^{''}} + 6 x^{^{'}} + 5 x = 0, x^{^{'}} (0) = 1, x (0) = 2

y^{^{''''}} - 6 y^{^{'''}} + 13 y^{^{''}} - 12 y^{^{'}} + 4 y = 0

2 y^{^{'''}} - y^{^{''}} - y^{^{'}} = 0

What is the solution for y^{''}+18y^'+82y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+18y^'+82y=0,y(0)=1,y^'(0)=0 is y=e^{-9t}(cos(t)+9sin(t))