What is the solution for y^{''}+6y^'+45y=6 ?

The solution for y^{''}+6y^'+45y=6 is y=e^{-3t}(c_{1}cos(6t)+c_{2}sin(6t))+2/15

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y^{''}+6y^'+45y=6

y^{^{''}} + 6 y^{^{'}} + 45 y = 6

y = e^{- 3 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{2}{15}

Solution steps

y^{''} (t) + 6 y^{'} (t) + 45 y = 6

Solve linear ODE:

y = e^{- 3 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{2}{15}

y = e^{- 3 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{2}{15}

2 y^{^{''}} + 3 y^{^{'}} + 5 y = 3 cos (5 t)

y^{^{''}} + 25 y = 4 cos (5 x) + 6 sin (5 x)

y^{^{''}} + 4 y - 4 = 0

y^{^{''}} + 2 y^{^{'}} + y = sin (t)

y^{^{''}} - 8 y^{^{'}} + 16 y = 12 e^{4 x}

What is the solution for y^{''}+6y^'+45y=6 ?
The solution for y^{''}+6y^'+45y=6 is y=e^{-3t}(c_{1}cos(6t)+c_{2}sin(6t))+2/15