What is the solution for y^{''}+y^'-2y=-2x^3-3x^2+8x+1 ?

The solution for y^{''}+y^'-2y=-2x^3-3x^2+8x+1 is y=c_{1}e^x+c_{2}e^{-2x}+x^3+3x^2+2x+7/2

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y^{''}+y^'-2y=-2x^3-3x^2+8x+1

y^{^{''}} + y^{^{'}} - 2 y = - 2 x^{3} - 3 x^{2} + 8 x + 1

y = c_{1} e^{x} + c_{2} e^{- 2 x} + x^{3} + 3 x^{2} + 2 x + \frac{7}{2}

Solution steps

y^{''} (x) + y^{'} (x) - 2 y = - 2 x^{3} - 3 x^{2} + 8 x + 1

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + x^{3} + 3 x^{2} + 2 x + \frac{7}{2}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + x^{3} + 3 x^{2} + 2 x + \frac{7}{2}

y^{^{''}} - 2 y^{^{'}} + 4 y = 4

y^{^{''}} + 2 y^{^{'}} = c

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 30, y (0) = 0, y^{^{'}} (0) = 0

q^{^{''}} + q^{^{'}} + \frac{1}{0.05} = 80 t

y^{^{''}} - y = - 11 t + 1

What is the solution for y^{''}+y^'-2y=-2x^3-3x^2+8x+1 ?
The solution for y^{''}+y^'-2y=-2x^3-3x^2+8x+1 is y=c_{1}e^x+c_{2}e^{-2x}+x^3+3x^2+2x+7/2