What is the solution for 3y^{''}+3y^'-6y=4e^{-2x} ?

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

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3y^{''}+3y^'-6y=4e^{-2x}

3 y^{^{''}} + 3 y^{^{'}} - 6 y = 4 e^{- 2 x}

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{4 e ^{- 2 x} x}{9}

Solution steps

3 y^{''} (x) + 3 y^{'} (x) - 6 y = 4 e^{- 2 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{4 e ^{- 2 x} x}{9}

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{4 e ^{- 2 x} x}{9}

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