What is the solution for y^{''}+4y^'=12x^2-10x-16 ?

The solution for y^{''}+4y^'=12x^2-10x-16 is y=c_{1}+c_{2}e^{-4x}+x^3-2x^2-3x

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y^{''}+4y^'=12x^2-10x-16

y^{^{''}} + 4 y^{^{'}} = 12 x^{2} - 10 x - 16

y = c_{1} + c_{2} e^{- 4 x} + x^{3} - 2 x^{2} - 3 x

Solution steps

y^{''} (x) + 4 y^{'} (x) = 12 x^{2} - 10 x - 16

Solve linear ODE:

y = c_{1} + c_{2} e^{- 4 x} + x^{3} - 2 x^{2} - 3 x

y = c_{1} + c_{2} e^{- 4 x} + x^{3} - 2 x^{2} - 3 x

(d^{2} + 6 d + 9) y = 5 e^{3} x

(d^{3} - 2 d^{2} - 3 d + 10) y = 40 cos (x)

y^{^{''}} + 3 y^{^{'}} + 2.25 y = 8 t^{3} + 64

(d^{2} + 4 d - 12) \cdot y = (x - 1) \cdot e^{2 x}

(d^{2} + 2 d + 10) y = 25 x^{2} + 3

What is the solution for y^{''}+4y^'=12x^2-10x-16 ?
The solution for y^{''}+4y^'=12x^2-10x-16 is y=c_{1}+c_{2}e^{-4x}+x^3-2x^2-3x