What is the solution for 2y^{''}+3y^'-2y=6x^2+5x-8 ?

The solution for 2y^{''}+3y^'-2y=6x^2+5x-8 is y=c_{1}e^{x/2}+c_{2}e^{-2x}-3x^2-(23x)/2-77/4

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2y^{''}+3y^'-2y=6x^2+5x-8

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 6 x^{2} + 5 x - 8

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 3 x^{2} - \frac{23 x}{2} - \frac{77}{4}

Solution steps

2 y^{''} (x) + 3 y^{'} (x) - 2 y = 6 x^{2} + 5 x - 8

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 3 x^{2} - \frac{23 x}{2} - \frac{77}{4}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 3 x^{2} - \frac{23 x}{2} - \frac{77}{4}

y^{^{''}} + 4 y = 2 cos (2 x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e^{x} - 3

y^{^{''}} + y^{^{'}} + y = x sin (x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 8 e^{x} - 9

5 y^{^{''}} - 10 y^{^{'}} + 10 y = e^{x} sec (x)

What is the solution for 2y^{''}+3y^'-2y=6x^2+5x-8 ?
The solution for 2y^{''}+3y^'-2y=6x^2+5x-8 is y=c_{1}e^{x/2}+c_{2}e^{-2x}-3x^2-(23x)/2-77/4