What is the solution for -2y^{''}+18y+2(3x^2+x+10/3)=0 ?

The solution for -2y^{''}+18y+2(3x^2+x+10/3)=0 is y=c_{1}e^{3x}+c_{2}e^{-3x}-(x^2)/3-x/9-4/9

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-2y^{''}+18y+2(3x^2+x+10/3)=0

- 2 y^{^{''}} + 18 y + 2 (3 x^{2} + x + \frac{10}{3}) = 0

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2}}{3} - \frac{x}{9} - \frac{4}{9}

Solution steps

- 2 y^{''} (x) + 18 y + 2 (3 x^{2} + x + \frac{10}{3}) = 0

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2}}{3} - \frac{x}{9} - \frac{4}{9}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{x ^{2}}{3} - \frac{x}{9} - \frac{4}{9}

What is the solution for -2y^{''}+18y+2(3x^2+x+10/3)=0 ?
The solution for -2y^{''}+18y+2(3x^2+x+10/3)=0 is y=c_{1}e^{3x}+c_{2}e^{-3x}-(x^2)/3-x/9-4/9