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

The solution for y^{''}-4y=6e^{-x} is y=c_{1}e^{2x}+c_{2}e^{-2x}-2e^{-x}

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int_{0}^{1} \frac{x}{x ^{2} + 1} d x

y^{4} x^{2} y^{^{'}} = 1

\frac{1}{( x + 4 ) ^{2}}

4 e^{x} cos (x)

ln (2 x) \cdot 4

What is the solution for y^{''}-4y=6e^{-x} ?
The solution for y^{''}-4y=6e^{-x} is y=c_{1}e^{2x}+c_{2}e^{-2x}-2e^{-x}