What is the solution for y^{''}+6y^'+9y=cos(3x) ?

The solution for y^{''}+6y^'+9y=cos(3x) is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+1/18 sin(3x)

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y^{''}+6y^'+9y=cos(3x)

y^{^{''}} + 6 y^{^{'}} + 9 y = cos (3 x)

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{1}{18} sin (3 x)

Solution steps

y^{''} (x) + 6 y^{'} (x) + 9 y = cos (3 x)

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{1}{18} sin (3 x)

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + \frac{1}{18} sin (3 x)

What is the solution for y^{''}+6y^'+9y=cos(3x) ?
The solution for y^{''}+6y^'+9y=cos(3x) is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+1/18 sin(3x)