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

The solution for (D-2)^2y=8e^{2x} is y=c_{1}e^{2x}+c_{2}xe^{2x}+4x^2e^{2x}

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

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

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + 4 x^{2} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + 4 x^{2} e^{2 x}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + 4 x^{2} e^{2 x}

y^{^{''}} - 10 y^{^{'}} + 25 y = 102 t^{2} e^{5 t}

2 y^{^{''}} + 4 y^{^{'}} + 8 y = 8

y^{^{''}} - 10 y^{^{'}} + 25 y = 30 x^{2} + 3

3 y^{^{''}} + 12 y = - 4 sin (2 t)

y^{^{''}} - y = x^{2} + 1, y (0) = 4, y (1) = 0

What is the solution for (D-2)^2y=8e^{2x} ?
The solution for (D-2)^2y=8e^{2x} is y=c_{1}e^{2x}+c_{2}xe^{2x}+4x^2e^{2x}