What is the solution for y^{''}-2y^'+y=4x^2-6+x-1ex ?

The solution for y^{''}-2y^'+y=4x^2-6+x-1ex is y=c_{1}e^x+c_{2}xe^x+4x^2+(-e+17)x-2e+20

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y^{''}-2y^'+y=4x^2-6+x-1ex

y^{^{''}} - 2 y^{^{'}} + y = 4 x^{2} - 6 + x - 1 e x

y = c_{1} e^{x} + c_{2} x e^{x} + 4 x^{2} + (- e + 17) x - 2 e + 20

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = 4 x^{2} - 6 + x - 1 e x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + 4 x^{2} + (- e + 17) x - 2 e + 20

y = c_{1} e^{x} + c_{2} x e^{x} + 4 x^{2} + (- e + 17) x - 2 e + 20

What is the solution for y^{''}-2y^'+y=4x^2-6+x-1ex ?
The solution for y^{''}-2y^'+y=4x^2-6+x-1ex is y=c_{1}e^x+c_{2}xe^x+4x^2+(-e+17)x-2e+20