What is the solution for y^{''}+6y^'+9y=-xe^{4x} ?

The solution for y^{''}+6y^'+9y=-xe^{4x} is y=c_{1}e^{-3x}+c_{2}xe^{-3x}-(e^{4x}x)/(49)+2/343 e^{4x}

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y^{''}+6y^'+9y=-xe^{4x}

y^{^{''}} + 6 y^{^{'}} + 9 y = - x e^{4 x}

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} - \frac{e ^{4 x} x}{49} + \frac{2}{343} e^{4 x}

Solution steps

y^{''} (x) + 6 y^{'} (x) + 9 y = - x e^{4 x}

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} - \frac{e ^{4 x} x}{49} + \frac{2}{343} e^{4 x}

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} - \frac{e ^{4 x} x}{49} + \frac{2}{343} e^{4 x}

\int \frac{8 x}{x ^{2} + x + 1} d x

x \to - 2 lim (x^{2} - 1)

\int (w + rs - \frac{1}{c} e^{(r - p) t}) d t

\frac{d}{d x} ((sin (3 x))^{l n (x)})

n \to \infty lim (\frac{3}{2})

What is the solution for y^{''}+6y^'+9y=-xe^{4x} ?
The solution for y^{''}+6y^'+9y=-xe^{4x} is y=c_{1}e^{-3x}+c_{2}xe^{-3x}-(e^{4x}x)/(49)+2/343 e^{4x}