What is the solution for (D^2-3D+2)y=xe^x ?

The solution for (D^2-3D+2)y=xe^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=xe^x

(D^{2} - 3 D + 2) y = x 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^{^{''}} + y = 8 sin (x) + 4 cos (x) + 1

x^{^{''}} + 4 x^{^{'}} + 4 = 0

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{( 1 + t ^{2} ) + 3 e ^{t}}

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

y^{^{''}} + 2 y^{^{'}} + 2 y = 4 cos (t) + 2 sin (t)

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