What is the solution for (d^2-4d-12)*y=(x-1)*e^{2x} ?

The solution for (d^2-4d-12)*y=(x-1)*e^{2x} is y=c_{1}e^{6x}+c_{2}e^{-2x}-(e^{2x}x)/(16)+1/16 e^{2x}

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(d^2-4d-12)y=(x-1)e^{2x}

(d^{2} - 4 d - 12) \cdot y = (x - 1) \cdot e^{2 x}

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{e ^{2 x} x}{16} + \frac{1}{16} e^{2 x}

Solution steps

(d^{2} - 4 d - 12) y = (x - 1) e^{2 x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{e ^{2 x} x}{16} + \frac{1}{16} e^{2 x}

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{e ^{2 x} x}{16} + \frac{1}{16} e^{2 x}

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

(d^{2} - 6 d + 9) y = 2 e^{3 x}

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

(d + 2) \cdot (d - 1)^{3} \cdot y = e^{x}

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 2 - 24 e^{x} + 40 e^{5} x

What is the solution for (d^2-4d-12)*y=(x-1)*e^{2x} ?
The solution for (d^2-4d-12)*y=(x-1)*e^{2x} is y=c_{1}e^{6x}+c_{2}e^{-2x}-(e^{2x}x)/(16)+1/16 e^{2x}