What is the solution for y^{''}-5y^'+6y=8xe^x ?

The solution for y^{''}-5y^'+6y=8xe^x is y=c_{1}e^{3x}+c_{2}e^{2x}+4xe^x+6e^x

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y^{''}-5y^'+6y=8xe^x

y^{^{''}} - 5 y^{^{'}} + 6 y = 8 x e^{x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + 4 x e^{x} + 6 e^{x}

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = 8 x e^{x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + 4 x e^{x} + 6 e^{x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + 4 x e^{x} + 6 e^{x}

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

y^{^{''}} + 3 y^{^{'}} = 1 - e^{- 3 x}

y^{^{''}} + 16 y = 6 x, y (0) = 1, y^{^{'}} (0) = 4

(D^{3} - 2 D^{2} - 3 D) y = 74 e^{- 3 x} cos (x)

y^{^{''}} - 2 y^{^{'}} - 3 y = - 11 t e^{- t}

What is the solution for y^{''}-5y^'+6y=8xe^x ?
The solution for y^{''}-5y^'+6y=8xe^x is y=c_{1}e^{3x}+c_{2}e^{2x}+4xe^x+6e^x