What is the solution for (D^2-3D+2)y=2x^3-9x^2+6x ?

The solution for (D^2-3D+2)y=2x^3-9x^2+6x is y=c_{1}e^{2x}+c_{2}e^x+x^3

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(D^2-3D+2)y=2x^3-9x^2+6x

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

y = c_{1} e^{2 x} + c_{2} e^{x} + x^{3}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + x^{3}

y = c_{1} e^{2 x} + c_{2} e^{x} + x^{3}

y^{^{''}} + 6 y^{^{'}} + 13 y = 7 cos (3 t + \frac{π}{4})

y^{^{''}} + 2 y^{^{'}} - 8 y = e^{2 t} + 5 t

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

y^{^{''}} - y^{^{'}} - 2 y = 2 e^{x}

(D^{2} - 4 D + 13) y = 24 e^{2 x} \cdot cos (3 x)

What is the solution for (D^2-3D+2)y=2x^3-9x^2+6x ?
The solution for (D^2-3D+2)y=2x^3-9x^2+6x is y=c_{1}e^{2x}+c_{2}e^x+x^3