What is the solution for y^{''}-9y=e^{3x} ?

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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