What is the solution for y^{''}-2y^'+y=xe^xsin(x) ?

The solution for y^{''}-2y^'+y=xe^xsin(x) is y=c_{1}e^x+c_{2}xe^x-e^xxsin(x)-2e^xcos(x)

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y^{''}-2y^'+y=xe^xsin(x)

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

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

Solution steps

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

Solve linear ODE:

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

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

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