What is the solution for (d^2-4)y=x^2 ?

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

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(d^2-4)y=x^2

(d^{2} - 4) y = x^{2}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{4} - \frac{1}{8}

Solution steps

(d^{2} - 4) y = x^{2}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{4} - \frac{1}{8}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{4} - \frac{1}{8}

y^{^{''}} - y = e^{x} + 1

2 y^{^{''}} + 6 y^{^{'}} - 20 y = 2 x - 3

y^{^{''}} - 4 y^{^{'}} + 4 y = sin (2 x)

y^{^{''}} - 4 y^{^{'}} - 32 y = 108 e^{2 t}

y^{^{''}} + 16 y = 32 sec (2 x)

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