What is the solution for (D^2-2D+1)y=xsin(x) ?

The solution for (D^2-2D+1)y=xsin(x) is y=c_{1}e^x+c_{2}xe^x+(xcos(x))/2+1/2 cos(x)-1/2 sin(x)

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(D^2-2D+1)y=xsin(x)

(D^{2} - 2 D + 1) y = x sin (x)

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{x cos ( x )}{2} + \frac{1}{2} cos (x) - \frac{1}{2} sin (x)

Solution steps

(D^{2} - 2 D + 1) y = x sin (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{x cos ( x )}{2} + \frac{1}{2} cos (x) - \frac{1}{2} sin (x)

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{x cos ( x )}{2} + \frac{1}{2} cos (x) - \frac{1}{2} sin (x)

y^{^{''}} + 4 y = sin (5 t), y (0) = 0, y^{^{'}} (0) = 0

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

y^{^{''}} + 3 y^{^{'}} - 10 y = 3 e^{- 5 x}

y^{^{''}} - 16 y = 80

y^{^{''}} + 10 y^{^{'}} + 25 y = (2 + 6 x) e^{- 5 x}

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