What is the solution for y^{''}+3y^'+2y=12x^2 ?

The solution for y^{''}+3y^'+2y=12x^2 is y=c_{1}e^{-x}+c_{2}e^{-2x}+6x^2-18x+21

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y^{''}+3y^'+2y=12x^2

y^{^{''}} + 3 y^{^{'}} + 2 y = 12 x^{2}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + 6 x^{2} - 18 x + 21

Solution steps

y^{''} (x) + 3 y^{'} (x) + 2 y = 12 x^{2}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + 6 x^{2} - 18 x + 21

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + 6 x^{2} - 18 x + 21

d (n) = 6 - 4 (n - 1)

y^{^{''}} - 2 y^{^{'}} + y = - e^{3 x} - e^{2 x}

y^{^{''}} - 4 y^{^{'}} + 5 y = 125 t^{2}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 18 y^{^{'}} + 45 y = e^{2 x} + x

y^{^{''}} + 16 y = 8 sec (4 x)

What is the solution for y^{''}+3y^'+2y=12x^2 ?
The solution for y^{''}+3y^'+2y=12x^2 is y=c_{1}e^{-x}+c_{2}e^{-2x}+6x^2-18x+21