What is the solution for 2y^{''}+3y^'-2y=14x^2-4x-11 ?

The solution for 2y^{''}+3y^'-2y=14x^2-4x-11 is y=c_{1}e^{x/2}+c_{2}e^{-2x}-7x^2-19x-37

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2y^{''}+3y^'-2y=14x^2-4x-11

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 14 x^{2} - 4 x - 11

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 7 x^{2} - 19 x - 37

Solution steps

2 y^{''} (x) + 3 y^{'} (x) - 2 y = 14 x^{2} - 4 x - 11

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 7 x^{2} - 19 x - 37

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - 7 x^{2} - 19 x - 37

4 y^{^{''}} - y = \frac{e x}{2 + 7}

4 y^{^{''}} - 4 y^{^{'}} + y = (- 3 x + 4) sin (x)

y^{^{''}} + 4 y = 2 sec^{3} (2 x)

y^{^{''}} + y^{^{'}} - 6 = 0

y^{^{''}} - 2 y^{^{'}} + 65 y = e^{x} cos (8 x)

What is the solution for 2y^{''}+3y^'-2y=14x^2-4x-11 ?
The solution for 2y^{''}+3y^'-2y=14x^2-4x-11 is y=c_{1}e^{x/2}+c_{2}e^{-2x}-7x^2-19x-37