What is the solution for (d-1)^2(d^2+1)y=3x^2-5x+2 ?

The solution for (d-1)^2(d^2+1)y=3x^2-5x+2 is y=c_{1}e^x+c_{2}xe^x+c_{3}cos(x)+c_{4}sin(x)+3x^2+7x+4

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(d-1)^2(d^2+1)y=3x^2-5x+2

(d - 1)^{2} (d^{2} + 1) y = 3 x^{2} - 5 x + 2

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} cos (x) + c_{4} sin (x) + 3 x^{2} + 7 x + 4

Solution steps

(d - 1)^{2} (d^{2} + 1) y = 3 x^{2} - 5 x + 2

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} cos (x) + c_{4} sin (x) + 3 x^{2} + 7 x + 4

y = c_{1} e^{x} + c_{2} x e^{x} + c_{3} cos (x) + c_{4} sin (x) + 3 x^{2} + 7 x + 4

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

(d^{2} - 13 d + 12) y = 2008

(d^{2} + 9) y = sec (3 x)

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{t}

(d^{2} - 3 d + 2) \cdot y = e^{5 x}

What is the solution for (d-1)^2(d^2+1)y=3x^2-5x+2 ?
The solution for (d-1)^2(d^2+1)y=3x^2-5x+2 is y=c_{1}e^x+c_{2}xe^x+c_{3}cos(x)+c_{4}sin(x)+3x^2+7x+4