What is the solution for y^{''}+8y^'+19y=0,y(0)=1,y^'(0)=2 ?

The solution for y^{''}+8y^'+19y=0,y(0)=1,y^'(0)=2 is y=e^{-4t}(cos(sqrt(3)t)+2sqrt(3)sin(sqrt(3)t))

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y^{''}+8y^'+19y=0,y(0)=1,y^'(0)=2

y^{^{''}} + 8 y^{^{'}} + 19 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y = e^{- 4 t} (cos (3 t) + 23 sin (3 t))

Solution steps

y^{''} (t) + 8 y^{'} (t) + 19 y = 0

Solve linear ODE:

y = e^{- 4 t} (cos (3 t) + 23 sin (3 t))

y = e^{- 4 t} (cos (3 t) + 23 sin (3 t))

What is the solution for y^{''}+8y^'+19y=0,y(0)=1,y^'(0)=2 ?
The solution for y^{''}+8y^'+19y=0,y(0)=1,y^'(0)=2 is y=e^{-4t}(cos(sqrt(3)t)+2sqrt(3)sin(sqrt(3)t))