What is the solution for (d^3-d^2-4d+4)y=e^3x ?

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

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(d^3-d^2-4d+4)y=e^3x

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

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{e ^{3} x}{4} + \frac{e ^{3}}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{e ^{3} x}{4} + \frac{e ^{3}}{4}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{e ^{3} x}{4} + \frac{e ^{3}}{4}

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

y^{^{''}} + 25 y = cos^{5} (x)

y^{^{'''}} + 3 y^{^{''}} + 3 y^{^{'}} + y = 30 e^{- x}

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3} x

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

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