What is the solution for y^{''}-y^'-6y=10xe^{3x}+17e^{3x} ?

The solution for y^{''}-y^'-6y=10xe^{3x}+17e^{3x} is y=c_{1}e^{3x}+c_{2}e^{-2x}+e^{3x}x^2+3e^{3x}x

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y^{''}-y^'-6y=10xe^{3x}+17e^{3x}

y^{^{''}} - y^{^{'}} - 6 y = 10 x e^{3 x} + 17 e^{3 x}

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

Solution steps

y^{''} (x) - y^{'} (x) - 6 y = 10 x e^{3 x} + 17 e^{3 x}

Solve linear ODE:

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

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

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

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

y^{^{''}} - 4 y^{^{'}} + 5 y = 10 x^{2} + 4 x + 8

y^{^{''}} + 2 y^{^{'}} + y = (\frac{1}{6}) (e^{- x})

y^{^{''}} + 9 y = 7 x, y (0) = 1, y^{^{'}} (0) = 3

What is the solution for y^{''}-y^'-6y=10xe^{3x}+17e^{3x} ?
The solution for y^{''}-y^'-6y=10xe^{3x}+17e^{3x} is y=c_{1}e^{3x}+c_{2}e^{-2x}+e^{3x}x^2+3e^{3x}x