What is the solution for y^{''}+6y^'+9y=6cos(t)+8sin(t) ?

The solution for y^{''}+6y^'+9y=6cos(t)+8sin(t) is y=c_{1}e^{-3t}+c_{2}te^{-3t}+sin(t)

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y^{''}+6y^'+9y=6cos(t)+8sin(t)

y^{^{''}} + 6 y^{^{'}} + 9 y = 6 cos (t) + 8 sin (t)

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

Solution steps

y^{''} (t) + 6 y^{'} (t) + 9 y = 6 cos (t) + 8 sin (t)

Solve linear ODE:

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

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

x \to 0 + lim ((1 - 8 x)^{\frac{1}{x}})

f (x) = x^{2} ln (7 x)

\frac{d}{d x} (e^{x s i n (x)})

\int (x^{2} x^{3} + 1) d x

\frac{d y}{d t} = 0.225 - 0.0045 y

What is the solution for y^{''}+6y^'+9y=6cos(t)+8sin(t) ?
The solution for y^{''}+6y^'+9y=6cos(t)+8sin(t) is y=c_{1}e^{-3t}+c_{2}te^{-3t}+sin(t)