What is the solution for y^{''}+3y^'=54x ?

The solution for y^{''}+3y^'=54x is y=c_{1}+c_{2}e^{-3x}+9x^2-6x

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y^{''}+3y^'=54x

y^{^{''}} + 3 y^{^{'}} = 54 x

y = c_{1} + c_{2} e^{- 3 x} + 9 x^{2} - 6 x

Solution steps

y^{''} (x) + 3 y^{'} (x) = 54 x

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 x} + 9 x^{2} - 6 x

y = c_{1} + c_{2} e^{- 3 x} + 9 x^{2} - 6 x

(D^{2} + 4 D + 5) y = 50 x + 13 e^{e x}

y^{^{''}} + 4 y^{^{'}} + 29 y = 2, y^{^{'}} (0) = 3

y^{^{''}} - 5 y^{^{'}} + 6 y = 4 e^{4 x}

y^{^{''}} + 2 y^{^{'}} + 3 y = 5 sin (4 t), y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} - 3 y^{^{'}} - 4 y = - 16 t, y (0) = - 4, y^{^{'}} (0) = - 5

What is the solution for y^{''}+3y^'=54x ?
The solution for y^{''}+3y^'=54x is y=c_{1}+c_{2}e^{-3x}+9x^2-6x