What is the solution for y^{''}+22y^'+122y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+22y^'+122y=0,y(0)=1,y^'(0)=0 is y=e^{-11t}(cos(t)+11sin(t))

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y^{''}+22y^'+122y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 22 y^{^{'}} + 122 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = e^{- 11 t} (cos (t) + 11 sin (t))

Solution steps

y^{''} (t) + 22 y^{'} (t) + 122 y = 0

Solve linear ODE:

y = e^{- 11 t} (cos (t) + 11 sin (t))

y = e^{- 11 t} (cos (t) + 11 sin (t))

4 y^{^{''}} + 20 y^{^{'}} + 169 y = 0

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = - 5, y^{^{'}} (0) = - 1

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

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

x^{^{''}} - 2 x^{^{'}} + x = 0

What is the solution for y^{''}+22y^'+122y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+22y^'+122y=0,y(0)=1,y^'(0)=0 is y=e^{-11t}(cos(t)+11sin(t))