What is the solution for y^{''}+8y^'+20y=0,y(0)=15,y^'(0)=-6 ?

The solution for y^{''}+8y^'+20y=0,y(0)=15,y^'(0)=-6 is y=e^{-4t}(15cos(2t)+27sin(2t))

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y^{''}+8y^'+20y=0,y(0)=15,y^'(0)=-6

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 15, y^{^{'}} (0) = - 6

y = e^{- 4 t} (15 cos (2 t) + 27 sin (2 t))

Solution steps

y^{''} (t) + 8 y^{'} (t) + 20 y = 0

Solve linear ODE:

y = e^{- 4 t} (15 cos (2 t) + 27 sin (2 t))

y = e^{- 4 t} (15 cos (2 t) + 27 sin (2 t))

What is the solution for y^{''}+8y^'+20y=0,y(0)=15,y^'(0)=-6 ?
The solution for y^{''}+8y^'+20y=0,y(0)=15,y^'(0)=-6 is y=e^{-4t}(15cos(2t)+27sin(2t))