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

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