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

The solution for 2y^{''}-6y=2x^2-x^2-x+3 is y=c_{1}e^{sqrt(3)x}+c_{2}e^{-sqrt(3)x}-(x^2)/6+x/6-11/18

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

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

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2}}{6} + \frac{x}{6} - \frac{11}{18}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2}}{6} + \frac{x}{6} - \frac{11}{18}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2}}{6} + \frac{x}{6} - \frac{11}{18}

What is the solution for 2y^{''}-6y=2x^2-x^2-x+3 ?
The solution for 2y^{''}-6y=2x^2-x^2-x+3 is y=c_{1}e^{sqrt(3)x}+c_{2}e^{-sqrt(3)x}-(x^2)/6+x/6-11/18