What is the solution for y^{''}+y^'-20y=e^x(82+84x-36x^2) ?

The solution for y^{''}+y^'-20y=e^x(82+84x-36x^2) is y=c_{1}e^{4x}+c_{2}e^{-5x}+2x^2e^x-4e^xx-5e^x

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y^{''}+y^'-20y=e^x(82+84x-36x^2)

y^{^{''}} + y^{^{'}} - 20 y = e^{x} (82 + 84 x - 36 x^{2})

y = c_{1} e^{4 x} + c_{2} e^{- 5 x} + 2 x^{2} e^{x} - 4 e^{x} x - 5 e^{x}

Solution steps

y^{''} (x) + y^{'} (x) - 20 y = e^{x} (82 + 84 x - 36 x^{2})

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 5 x} + 2 x^{2} e^{x} - 4 e^{x} x - 5 e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 5 x} + 2 x^{2} e^{x} - 4 e^{x} x - 5 e^{x}

What is the solution for y^{''}+y^'-20y=e^x(82+84x-36x^2) ?
The solution for y^{''}+y^'-20y=e^x(82+84x-36x^2) is y=c_{1}e^{4x}+c_{2}e^{-5x}+2x^2e^x-4e^xx-5e^x