What is the solution for 9y^{''}-12y^'+4y=e^{-3x} ?

The solution for 9y^{''}-12y^'+4y=e^{-3x} is y=c_{1}e^{(2x)/3}+c_{2}e^{(2x)/3}x+1/121 e^{-3x}

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9y^{''}-12y^'+4y=e^{-3x}

9 y^{^{''}} - 12 y^{^{'}} + 4 y = e^{- 3 x}

y = c_{1} e^{\frac{2 x}{3}} + c_{2} e^{\frac{2 x}{3}} x + \frac{1}{121} e^{- 3 x}

Solution steps

9 y^{''} (x) - 12 y^{'} (x) + 4 y = e^{- 3 x}

Solve linear ODE:

y = c_{1} e^{\frac{2 x}{3}} + c_{2} e^{\frac{2 x}{3}} x + \frac{1}{121} e^{- 3 x}

y = c_{1} e^{\frac{2 x}{3}} + c_{2} e^{\frac{2 x}{3}} x + \frac{1}{121} e^{- 3 x}

\int \frac{e ^{x}}{e ^{x} + e ^{2 x} - 2} d x

\frac{d}{d x} (x^{2} + 8)

(x + y) d x + x ln (x) d y = 0

\frac{\partial}{\partial y} (x e^{x y})

x \to 7 lim (tan (\frac{π x}{6}))

What is the solution for 9y^{''}-12y^'+4y=e^{-3x} ?
The solution for 9y^{''}-12y^'+4y=e^{-3x} is y=c_{1}e^{(2x)/3}+c_{2}e^{(2x)/3}x+1/121 e^{-3x}