What is the solution for y^{''}-2y^'+y=x^3+9x ?

The solution for y^{''}-2y^'+y=x^3+9x is y=c_{1}e^x+c_{2}xe^x+x^3+6x^2+27x+42

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y^{''}-2y^'+y=x^3+9x

y^{^{''}} - 2 y^{^{'}} + y = x^{3} + 9 x

y = c_{1} e^{x} + c_{2} x e^{x} + x^{3} + 6 x^{2} + 27 x + 42

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + x^{3} + 6 x^{2} + 27 x + 42

y = c_{1} e^{x} + c_{2} x e^{x} + x^{3} + 6 x^{2} + 27 x + 42

y^{^{''}} + 6 y^{^{'}} + 9 y = 4 e^{- 3 x} + 50 sin (x)

y^{^{''}} - 8 y^{^{'}} + 25 y = 4 x^{3} e^{- x} - 7 e^{- x}

y^{^{''}} + 9 y = x - 2 cos (3 x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 t

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

What is the solution for y^{''}-2y^'+y=x^3+9x ?
The solution for y^{''}-2y^'+y=x^3+9x is y=c_{1}e^x+c_{2}xe^x+x^3+6x^2+27x+42