What is the solution for D^2(D-1)y=8e^{2x} ?

The solution for D^2(D-1)y=8e^{2x} is y=c_{1}e^x+c_{2}+c_{3}x+2e^{2x}

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D^2(D-1)y=8e^{2x}

D^{2} (D - 1) y = 8 e^{2 x}

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

Solution steps

D^{2} (D - 1) y = 8 e^{2 x}

Solve linear ODE:

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

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

x^{^{''}} - x^{^{'}} - 6 x = 2 e^{4 t}

y^{^{''}} + a y = b

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

y^{^{''}} + 25 y = 3 x, y (0) = 1, y^{^{'}} (0) = 5

y^{^{'''}} + 7 y^{^{''}} + 15 y^{^{'}} + 9 = 1

What is the solution for D^2(D-1)y=8e^{2x} ?
The solution for D^2(D-1)y=8e^{2x} is y=c_{1}e^x+c_{2}+c_{3}x+2e^{2x}