What is the solution for y^{''}-2y^'+y=x^3+7x ?

The solution for y^{''}-2y^'+y=x^3+7x is y=c_{1}e^x+c_{2}xe^x+x^3+6x^2+25x+38

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y^{''}-2y^'+y=x^3+7x

y^{^{''}} - 2 y^{^{'}} + y = x^{3} + 7 x

y = c_{1} e^{x} + c_{2} x e^{x} + x^{3} + 6 x^{2} + 25 x + 38

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = x^{3} + 7 x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + x^{3} + 6 x^{2} + 25 x + 38

y = c_{1} e^{x} + c_{2} x e^{x} + x^{3} + 6 x^{2} + 25 x + 38

y^{^{''}} + 6 y^{^{'}} + 34 y = 68

x^{^{''}} + 16 x = cos (2 t)

(8 x^{^{''}} + 4 x^{^{'}} - 24) = 48 e^{2 t}

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

2 y^{^{''}} + y^{^{'}} - y = 3 x + 4

What is the solution for y^{''}-2y^'+y=x^3+7x ?
The solution for y^{''}-2y^'+y=x^3+7x is y=c_{1}e^x+c_{2}xe^x+x^3+6x^2+25x+38