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

The solution for y^{''}-2y^'+y=4x^2-4+x-1ex is y=c_{1}e^x+c_{2}xe^x+4x^2+(-e+17)x-2e+22

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

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

y = c_{1} e^{x} + c_{2} x e^{x} + 4 x^{2} + (- e + 17) x - 2 e + 22

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = 4 x^{2} - 4 + 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 + 22

y = c_{1} e^{x} + c_{2} x e^{x} + 4 x^{2} + (- e + 17) x - 2 e + 22

y^{^{''}} - 36 y = - 108 t + 72 t^{2}

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 3 y = 4 e^{x} - 9

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = cos (2 x)

x^{^{''}} + 2 x = cos (8 t)

y^{^{''}} + 12 y^{^{'}} + 37 = 0, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for y^{''}-2y^'+y=4x^2-4+x-1ex ?
The solution for y^{''}-2y^'+y=4x^2-4+x-1ex is y=c_{1}e^x+c_{2}xe^x+4x^2+(-e+17)x-2e+22