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

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

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

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

y = c_{1} e^{- x} + c_{2} e^{x} + c_{3} x e^{x} - \frac{2}{9} e^{- 2 x} + 3

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{x} + c_{3} x e^{x} - \frac{2}{9} e^{- 2 x} + 3

y = c_{1} e^{- x} + c_{2} e^{x} + c_{3} x e^{x} - \frac{2}{9} e^{- 2 x} + 3

x^{^{''}} - 4 x^{^{'}} + 4 x = e^{2 t}, x (0) = 2, x^{^{'}} (0) = 1

y^{^{'''}} + 256 y^{^{'}} = tan (16 x)

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

y^{^{''}} + 6 y^{^{'}} + 5 y = 10

y^{^{''}} + 6 y^{^{'}} + 5 y = 15

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