What is the solution for y^{''}+6y^'+9y=e^{2x}(3-5x) ?

The solution for y^{''}+6y^'+9y=e^{2x}(3-5x) is y=c_{1}e^{-3x}+c_{2}xe^{-3x}-(e^{2x}x)/5+1/5 e^{2x}

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y^{''}+6y^'+9y=e^{2x}(3-5x)

y^{^{''}} + 6 y^{^{'}} + 9 y = e^{2 x} (3 - 5 x)

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} - \frac{e ^{2 x} x}{5} + \frac{1}{5} e^{2 x}

Solution steps

y^{''} (x) + 6 y^{'} (x) + 9 y = e^{2 x} (3 - 5 x)

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} - \frac{e ^{2 x} x}{5} + \frac{1}{5} e^{2 x}

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} - \frac{e ^{2 x} x}{5} + \frac{1}{5} e^{2 x}

\int \frac{x + 4}{2 x ^{2} + x - 1} d x

f (x) = x + 15, at x = 1

(3 x^{2}) d x + (2 y - 4 x^{3} y^{- 1}) d y = 0

\int x sin^{2} (5 x) d x

\frac{d y}{d t} = 1 y

What is the solution for y^{''}+6y^'+9y=e^{2x}(3-5x) ?
The solution for y^{''}+6y^'+9y=e^{2x}(3-5x) is y=c_{1}e^{-3x}+c_{2}xe^{-3x}-(e^{2x}x)/5+1/5 e^{2x}