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

The solution for (d^2-3d)y=x^2+2x-6 is y=c_{1}e^{3x}+c_{2}-(x^3)/9-(4x^2)/9+(46x)/(27)

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(d^2-3d)y=x^2+2x-6

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

y = c_{1} e^{3 x} + c_{2} - \frac{x ^{3}}{9} - \frac{4 x ^{2}}{9} + \frac{46 x}{27}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} - \frac{x ^{3}}{9} - \frac{4 x ^{2}}{9} + \frac{46 x}{27}

y = c_{1} e^{3 x} + c_{2} - \frac{x ^{3}}{9} - \frac{4 x ^{2}}{9} + \frac{46 x}{27}

y^{^{''}} + y = - 8 x cos (x)

x^{^{''}} - x^{^{'}} - 12 x = 2 sinh^{2} (t)

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

(D^{2} - 2 D) y = e^{x} sin (x)

y^{^{''}} - 81 y = 9, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for (d^2-3d)y=x^2+2x-6 ?
The solution for (d^2-3d)y=x^2+2x-6 is y=c_{1}e^{3x}+c_{2}-(x^3)/9-(4x^2)/9+(46x)/(27)