What is the solution for y^{''}-4y=e^{-2x}-2x ?

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

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y^{''}-4y=e^{-2x}-2x

y^{^{''}} - 4 y = e^{- 2 x} - 2 x

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

Solution steps

y^{''} (x) - 4 y = e^{- 2 x} - 2 x

Solve linear ODE:

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

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

\int cos (10 x) cos (3 x) d x

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

1500 e^{x}

\frac{d}{d x} (\frac{x ^{2}}{x + 1})

y^{^{'}} + \frac{y}{t} = 2 cos (3 t)

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