What is the solution for y^{''}+8y^'+20y=0,y(0)=1,y^'(0)=7 ?

The solution for y^{''}+8y^'+20y=0,y(0)=1,y^'(0)=7 is y=e^{-4t}(cos(2t)+11/2 sin(2t))

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y^{''}+8y^'+20y=0,y(0)=1,y^'(0)=7

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 1, y^{^{'}} (0) = 7

y = e^{- 4 t} (cos (2 t) + \frac{11}{2} sin (2 t))

Solution steps

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

Solve linear ODE:

y = e^{- 4 t} (cos (2 t) + \frac{11}{2} sin (2 t))

y = e^{- 4 t} (cos (2 t) + \frac{11}{2} sin (2 t))

What is the solution for y^{''}+8y^'+20y=0,y(0)=1,y^'(0)=7 ?
The solution for y^{''}+8y^'+20y=0,y(0)=1,y^'(0)=7 is y=e^{-4t}(cos(2t)+11/2 sin(2t))