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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

(D^{4} + 10 D^{2} + 9) y = sin (3 x) + cos (3 x)

y^{^{''}} + 36 y = 2 e^{6 x}

y^{^{''}} + 2 y^{^{'}} - 8 y = 2 e^{4 t}

d (x) = \frac{3}{2 x}

(d^{2} + 6 d + 9) y = \frac{e ^{- 3} x}{x ^{3}}

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