What is the solution for y^{''}-y^'-6y=e^{-2x} ?

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

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y^{''}-y^'-6y=e^{-2x}

y^{^{''}} - y^{^{'}} - 6 y = e^{- 2 x}

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

Solution steps

y^{''} (x) - y^{'} (x) - 6 y = e^{- 2 x}

Solve linear ODE:

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

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

f (x) = \frac{2 x - 3}{2 x + 5}, at x = - 1

x \to 0 lim (3 x^{2} - 4 x + 5)

\int_{1}^{2} x 5^{x^{2}} d x

\int e^{- j wt} d t

\frac{d}{d x} (4 x^{3} - sin (x))

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