What is the solution for y^{''}+8y^'+16y=6cos(4t) ?

The solution for y^{''}+8y^'+16y=6cos(4t) is y=c_{1}e^{-4t}+c_{2}te^{-4t}+3/16 sin(4t)

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y^{''}+8y^'+16y=6cos(4t)

y^{^{''}} + 8 y^{^{'}} + 16 y = 6 cos (4 t)

y = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} + \frac{3}{16} sin (4 t)

Solution steps

y^{''} (t) + 8 y^{'} (t) + 16 y = 6 cos (4 t)

Solve linear ODE:

y = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} + \frac{3}{16} sin (4 t)

y = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} + \frac{3}{16} sin (4 t)

What is the solution for y^{''}+8y^'+16y=6cos(4t) ?
The solution for y^{''}+8y^'+16y=6cos(4t) is y=c_{1}e^{-4t}+c_{2}te^{-4t}+3/16 sin(4t)