What is the solution for y^{''}+3y^'+2y=-6-4x-7x^2-2x^3 ?

The solution for y^{''}+3y^'+2y=-6-4x-7x^2-2x^3 is y=c_{1}e^{-x}+c_{2}e^{-2x}-x^3+x^2-2x-1

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y^{''}+3y^'+2y=-6-4x-7x^2-2x^3

y^{^{''}} + 3 y^{^{'}} + 2 y = - 6 - 4 x - 7 x^{2} - 2 x^{3}

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

Solution steps

y^{''} (x) + 3 y^{'} (x) + 2 y = - 6 - 4 x - 7 x^{2} - 2 x^{3}

Solve linear ODE:

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

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

(D^{2} + 1) y = 12 cos^{2} (x)

(D^{2} + 3 D + 2) y = 1 + 3 x + x^{2}

y^{^{''}} - 4 y = cos (x) - sin (x)

y^{^{''}} + 8 y^{^{'}} + 12 y = x e^{2 x}

x^{^{''}} + 2 x^{^{'}} + 1 x = e^{- 2 t}

What is the solution for y^{''}+3y^'+2y=-6-4x-7x^2-2x^3 ?
The solution for y^{''}+3y^'+2y=-6-4x-7x^2-2x^3 is y=c_{1}e^{-x}+c_{2}e^{-2x}-x^3+x^2-2x-1