What is the solution for y^{''}+6y^'+9y=12e^{-x} ?

The solution for y^{''}+6y^'+9y=12e^{-x} is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+3e^{-x}

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y^{''}+6y^'+9y=12e^{-x}

y^{^{''}} + 6 y^{^{'}} + 9 y = 12 e^{- x}

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + 3 e^{- x}

Solution steps

y^{''} (x) + 6 y^{'} (x) + 9 y = 12 e^{- x}

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + 3 e^{- x}

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + 3 e^{- x}

\frac{d}{d x} (cos (\frac{1 - e ^{8 x}}{1 + e ^{8 x}}))

\int \frac{z}{1 0 ^{z}} d z

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

x \to 2 + lim (\frac{x - 2}{∣ x - 2 ∣})

x e^{x} ln (y + 1) d x + (x + 1)^{2} (\frac{1}{y + 1}) d y = 0

What is the solution for y^{''}+6y^'+9y=12e^{-x} ?
The solution for y^{''}+6y^'+9y=12e^{-x} is y=c_{1}e^{-3x}+c_{2}xe^{-3x}+3e^{-x}