What is the solution for D(D-1)^3(y)=(x^2+2x)e^x ?

The solution for D(D-1)^3(y)=(x^2+2x)e^x is y=c_{1}+c_{2}e^x+c_{3}xe^x+c_{4}x^2e^x+(e^xx^5)/(60)

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D(D-1)^3(y)=(x^2+2x)e^x

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

y = c_{1} + c_{2} e^{x} + c_{3} x e^{x} + c_{4} x^{2} e^{x} + \frac{e ^{x} x ^{5}}{60}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{x} + c_{3} x e^{x} + c_{4} x^{2} e^{x} + \frac{e ^{x} x ^{5}}{60}

y = c_{1} + c_{2} e^{x} + c_{3} x e^{x} + c_{4} x^{2} e^{x} + \frac{e ^{x} x ^{5}}{60}

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

y^{^{''}} + y^{^{'}} + 64 y = 5 cos (2 t)

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

y^{^{'''}} + 9 y^{^{'}} = tan (3 x)

y^{^{''}} - y^{^{'}} + 14 y = \frac{4 + e x}{2}

What is the solution for D(D-1)^3(y)=(x^2+2x)e^x ?
The solution for D(D-1)^3(y)=(x^2+2x)e^x is y=c_{1}+c_{2}e^x+c_{3}xe^x+c_{4}x^2e^x+(e^xx^5)/(60)