What is the solution for y^{''}+y^'-6y=6x^2-2x-2 ?

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

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y^{''}+y^'-6y=6x^2-2x-2

y^{^{''}} + y^{^{'}} - 6 y = 6 x^{2} - 2 x - 2

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

Solution steps

y^{''} (x) + y^{'} (x) - 6 y = 6 x^{2} - 2 x - 2

Solve linear ODE:

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

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

y^{^{''}} + 4 y = x^{23} e^{x}

(d^{2} - 4 d + 4) \cdot y = x^{3}

(d^{3} - 25 d) y = sin^{2} (x) cos^{2} (x)

(d^{3} - 3 d - 2) y = x^{3}

y^{^{''}} + y^{^{'}} - 2 y = 14 + 2 x - 2 x^{2}

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