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) \cdot 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}

(d^{2} - 2 d + 1) \cdot y = cos^{2} (x) + x^{2}

y^{^{''}} + y^{^{'}} + 3 y = 9 x^{2} + 3

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

(d^{2} - 4 d + 1) y = e^{2} x sin (x)

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