What is the solution for y^{'''}-5y^{''}+6y^'=6e^{2x}-2 ?

The solution for y^{'''}-5y^{''}+6y^'=6e^{2x}-2 is y=c_{1}+c_{2}e^{2x}+c_{3}e^{3x}-3xe^{2x}-x/3

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y^{'''}-5y^{''}+6y^'=6e^{2x}-2

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 6 e^{2 x} - 2

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

Solution steps

y^{'''} (x) - 5 y^{''} (x) + 6 y^{'} (x) = 6 e^{2 x} - 2

Solve linear ODE:

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

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

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

y^{^{''}} + 2 y = 8 x + 5

y^{^{''}} + 9 y^{^{'}} = cos (3 t)

(D^{2} + 2 D + 1) y = x e^{- x}

\frac{d ^{2} y}{d x ^{2}} - y = 1

What is the solution for y^{'''}-5y^{''}+6y^'=6e^{2x}-2 ?
The solution for y^{'''}-5y^{''}+6y^'=6e^{2x}-2 is y=c_{1}+c_{2}e^{2x}+c_{3}e^{3x}-3xe^{2x}-x/3