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

The solution for y^{'''}+2y^{''}-y^'-2y=e^{2x} is y=c_{1}e^{-2x}+c_{2}e^{-x}+c_{3}e^x+1/12 e^{2x}

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

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

y = c_{1} e^{- 2 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{12} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{12} e^{2 x}

y = c_{1} e^{- 2 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{1}{12} e^{2 x}

What is the solution for y^{'''}+2y^{''}-y^'-2y=e^{2x} ?
The solution for y^{'''}+2y^{''}-y^'-2y=e^{2x} is y=c_{1}e^{-2x}+c_{2}e^{-x}+c_{3}e^x+1/12 e^{2x}