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

The solution for (d^2-4d+3)y=x^3 is y=c_{1}e^{3x}+c_{2}e^x+(x^3)/3+(4x^2)/3+(26x)/9+80/27

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

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

y = c_{1} e^{3 x} + c_{2} e^{x} + \frac{x ^{3}}{3} + \frac{4 x ^{2}}{3} + \frac{26 x}{9} + \frac{80}{27}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{x} + \frac{x ^{3}}{3} + \frac{4 x ^{2}}{3} + \frac{26 x}{9} + \frac{80}{27}

y = c_{1} e^{3 x} + c_{2} e^{x} + \frac{x ^{3}}{3} + \frac{4 x ^{2}}{3} + \frac{26 x}{9} + \frac{80}{27}

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

y, (d^{3} + d) \cdot y = cos (t) + t^{2} + 3

y^{^{''}} + 2 y^{^{'}} - 3 y = e^{2} x

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

y^{^{''}} - 2 y^{^{'}} - 8 y = 5 e^{2} x

What is the solution for (d^2-4d+3)y=x^3 ?
The solution for (d^2-4d+3)y=x^3 is y=c_{1}e^{3x}+c_{2}e^x+(x^3)/3+(4x^2)/3+(26x)/9+80/27