What is the solution for (d^2-2d+1)*y=x*e^x*cos(x) ?

The solution for (d^2-2d+1)*y=x*e^x*cos(x) is y=c_{1}e^x+c_{2}xe^x-e^xxcos(x)+2e^xsin(x)

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(d^2-2d+1)y=xe^x*cos(x)

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

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

Solution steps

(d^{2} - 2 d + 1) y = x e^{x} cos (x)

Solve linear ODE:

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

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

d^{2} (d^{2} + 1) y = 1

y^{^{'''}} + 3 y^{^{''}} = - 36 x^{2} + 12 x + 42

y^{^{''}} - y^{^{'}} = e^{2 x} \cdot cos (e^{x})

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x^{2} + 3 + 2 cos^{2} (x)

y^{^{''}} - 3 y^{^{'}} + 10 y = cosh (2 x)

What is the solution for (d^2-2d+1)*y=x*e^x*cos(x) ?
The solution for (d^2-2d+1)*y=x*e^x*cos(x) is y=c_{1}e^x+c_{2}xe^x-e^xxcos(x)+2e^xsin(x)