What is the solution for 2y^{''}+3y^'-2y=10x^2-4x-13 ?

The solution for 2y^{''}+3y^'-2y=10x^2-4x-13 is y=c_{1}e^{x/2}+c_{2}e^{-2x}-5x^2-13x-23

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2y^{''}+3y^'-2y=10x^2-4x-13

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 10 x^{2} - 4 x - 13

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 5 x^{2} - 13 x - 23

Solution steps

2 y^{''} (x) + 3 y^{'} (x) - 2 y = 10 x^{2} - 4 x - 13

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 5 x^{2} - 13 x - 23

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 5 x^{2} - 13 x - 23

y^{^{''}} + 2 y^{^{'}} = t e^{- t}, y (0) = 6, y^{^{'}} (0) = - 1

y^{^{''}} - 5 y^{^{'}} = 3 e^{5 t} - 7 t + 4

e^{x} y^{^{''}} + 2 e^{x} y^{^{'}} + e^{x} y = ln (x)

y^{^{'''}} + y^{^{''}} = 4 x + e^{- x}

y^{^{''}} - 6 y^{^{'}} + 9 y = - 12 e^{3 x}

What is the solution for 2y^{''}+3y^'-2y=10x^2-4x-13 ?
The solution for 2y^{''}+3y^'-2y=10x^2-4x-13 is y=c_{1}e^{x/2}+c_{2}e^{-2x}-5x^2-13x-23