What is the solution for y^{''}-2y^'+y=5xe^xsin(x) ?

The solution for y^{''}-2y^'+y=5xe^xsin(x) is y=c_{1}e^x+c_{2}xe^x-5e^xxsin(x)-10e^xcos(x)

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y^{''}-2y^'+y=5xe^xsin(x)

y^{^{''}} - 2 y^{^{'}} + y = 5 x e^{x} sin (x)

y = c_{1} e^{x} + c_{2} x e^{x} - 5 e^{x} x sin (x) - 10 e^{x} cos (x)

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = 5 x e^{x} sin (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - 5 e^{x} x sin (x) - 10 e^{x} cos (x)

y = c_{1} e^{x} + c_{2} x e^{x} - 5 e^{x} x sin (x) - 10 e^{x} cos (x)

y^{^{''}} + 4 y^{^{'}} + 3 y = 6 + e^{2 t}

y^{^{''}} + 12 y^{^{'}} + 37 y = 4 H (t)

y^{^{''}} - y^{^{'}} + 441 y = 21 sin (21 t)

y^{^{''}} - 2 y^{^{'}} + 5 y = 4 e^{x} sin (2 x) + 5 x

y^{^{''}} + 2 y^{^{'}} + 5 y = 4 e^{- t} \cdot cos (2 t)

What is the solution for y^{''}-2y^'+y=5xe^xsin(x) ?
The solution for y^{''}-2y^'+y=5xe^xsin(x) is y=c_{1}e^x+c_{2}xe^x-5e^xxsin(x)-10e^xcos(x)