What is the solution for 9y^{''}-y=(xex)/3 ?

The solution for 9y^{''}-y=(xex)/3 is y=c_{1}e^{x/3}+c_{2}e^{-x/3}-(ex^2)/3-6e

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9y^{''}-y=(xex)/3

9 y^{^{''}} - y = \frac{x e x}{3}

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

Solution steps

9 y^{''} (x) - y = \frac{x e x}{3}

Solve linear ODE:

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

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

What is the solution for 9y^{''}-y=(xex)/3 ?
The solution for 9y^{''}-y=(xex)/3 is y=c_{1}e^{x/3}+c_{2}e^{-x/3}-(ex^2)/3-6e