What is the solution for 2y^{''}+3y^'-2y=10x^2-4x-15 ?

The solution for 2y^{''}+3y^'-2y=10x^2-4x-15 is y=c_{1}e^{x/2}+c_{2}e^{-2x}-5x^2-13x-22

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2y^{''}+3y^'-2y=10x^2-4x-15

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 10 x^{2} - 4 x - 15

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 5 x^{2} - 13 x - 22

Solution steps

2 y^{''} (x) + 3 y^{'} (x) - 2 y = 10 x^{2} - 4 x - 15

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 5 x^{2} - 13 x - 22

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 5 x^{2} - 13 x - 22

x^{^{'''}} + 10 x^{^{''}} + 33 x^{^{'}} + 36 x = 4 t e^{- 3 t}

y^{^{''}} - 6 y^{^{'}} + 9 y = 12 e^{t} sin (t)

y^{^{''}} + 4 y = - 16 sin (2 t)

y^{^{''}} + 4 y^{^{'}} + 13 y = 52, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 e^{2 x}

What is the solution for 2y^{''}+3y^'-2y=10x^2-4x-15 ?
The solution for 2y^{''}+3y^'-2y=10x^2-4x-15 is y=c_{1}e^{x/2}+c_{2}e^{-2x}-5x^2-13x-22