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

The solution for (d^2-3d+2)y=x*e^x is y=c_{1}e^{2x}+c_{2}e^x-(e^xx^2)/2-e^xx

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(d^2-3d+2)y=x*e^x

(d^{2} - 3 d + 2) y = x \cdot e^{x}

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{e ^{x} x ^{2}}{2} - e^{x} x

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{e ^{x} x ^{2}}{2} - e^{x} x

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{e ^{x} x ^{2}}{2} - e^{x} x

y^{^{''}} - 4 y^{^{'}} + 4 y = 12 e^{2 x} + x^{2}

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

(d^{4} - 2 d^{2} + 1) \cdot y = cos (x)

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

y^{^{''}} + 2 y^{^{'}} + (\frac{3}{4}) y = 3 e^{x} + (\frac{9}{2}) x

What is the solution for (d^2-3d+2)y=x*e^x ?
The solution for (d^2-3d+2)y=x*e^x is y=c_{1}e^{2x}+c_{2}e^x-(e^xx^2)/2-e^xx