What is the solution for y^{''}-9y^'=81x^2+7 ?

The solution for y^{''}-9y^'=81x^2+7 is y=c_{1}e^{9x}+c_{2}-3x^3-x^2-x

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y^{''}-9y^'=81x^2+7

y^{^{''}} - 9 y^{^{'}} = 81 x^{2} + 7

y = c_{1} e^{9 x} + c_{2} - 3 x^{3} - x^{2} - x

Solution steps

y^{''} (x) - 9 y^{'} (x) = 81 x^{2} + 7

Solve linear ODE:

y = c_{1} e^{9 x} + c_{2} - 3 x^{3} - x^{2} - x

y = c_{1} e^{9 x} + c_{2} - 3 x^{3} - x^{2} - x

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

- y^{^{''}} + 10 y^{^{'}} + 25 y = 30 x + 3

y^{^{''}} + 4 y = 5 sec (2 x)

y^{^{''}} + y = e^{t} + t^{3}, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 e^{- 2 t}

What is the solution for y^{''}-9y^'=81x^2+7 ?
The solution for y^{''}-9y^'=81x^2+7 is y=c_{1}e^{9x}+c_{2}-3x^3-x^2-x