What is the solution for y^{''}+10y^'+16y=2581cos(5t) ?

The solution for y^{''}+10y^'+16y=2581cos(5t) is y=c_{1}e^{-2t}+c_{2}e^{-8t}+50sin(5t)-9cos(5t)

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y^{''}+10y^'+16y=2581cos(5t)

y^{^{''}} + 10 y^{^{'}} + 16 y = 2581 cos (5 t)

y = c_{1} e^{- 2 t} + c_{2} e^{- 8 t} + 50 sin (5 t) - 9 cos (5 t)

Solution steps

y^{''} (t) + 10 y^{'} (t) + 16 y = 2581 cos (5 t)

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 8 t} + 50 sin (5 t) - 9 cos (5 t)

y = c_{1} e^{- 2 t} + c_{2} e^{- 8 t} + 50 sin (5 t) - 9 cos (5 t)

y^{^{''}} = k y - c

y^{^{''}} + 2 y^{^{'}} = sec (x)

y^{^{''}} - y^{^{'}} - 2 y = \frac{e ^{2 t} + e ^{- 2 t}}{2}

y^{^{'''}} + 144 y^{^{'}} = tan (12 x)

y^{^{''}} - 4 y^{^{'}} + 3 y = e^{4 x} (- 8 + 29 x + 12 x^{2})

What is the solution for y^{''}+10y^'+16y=2581cos(5t) ?
The solution for y^{''}+10y^'+16y=2581cos(5t) is y=c_{1}e^{-2t}+c_{2}e^{-8t}+50sin(5t)-9cos(5t)