What is the solution for 2y^{''}+3y^'-2y=10x^2-8x-15 ?

The solution for 2y^{''}+3y^'-2y=10x^2-8x-15 is y=c_{1}e^{x/2}+c_{2}e^{-2x}-5x^2-11x-19

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2y^{''}+3y^'-2y=10x^2-8x-15

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 10 x^{2} - 8 x - 15

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 5 x^{2} - 11 x - 19

Solution steps

2 y^{''} (x) + 3 y^{'} (x) - 2 y = 10 x^{2} - 8 x - 15

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 5 x^{2} - 11 x - 19

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 5 x^{2} - 11 x - 19

What is the solution for 2y^{''}+3y^'-2y=10x^2-8x-15 ?
The solution for 2y^{''}+3y^'-2y=10x^2-8x-15 is y=c_{1}e^{x/2}+c_{2}e^{-2x}-5x^2-11x-19