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

The solution for d*e(d^2-4)y=(e^2)^x is y=c_{1}+c_{2}e^{-2x}+c_{3}e^{2x}+(e^{2x-1}x)/8

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

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

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{e ^{2 x - 1} x}{8}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{e ^{2 x - 1} x}{8}

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{e ^{2 x - 1} x}{8}

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

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 cosh (x)

(d^{2} - 4 d + 4) y = 8 x^{2} e^{2} x sin^{2} (x)

(d^{3} - 6 d^{2} + 11 d - 6) y = e - 2 x + e - 3 x

(d^{2} + 4) y = sin^{3} (x)

What is the solution for d*e(d^2-4)y=(e^2)^x ?
The solution for d*e(d^2-4)y=(e^2)^x is y=c_{1}+c_{2}e^{-2x}+c_{3}e^{2x}+(e^{2x-1}x)/8