What is the solution for y^{''}-81y=e^{9x} ?

The solution for y^{''}-81y=e^{9x} is y=c_{1}e^{9x}+c_{2}e^{-9x}+(e^{9x}x)/(18)

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y^{''}-81y=e^{9x}

y^{^{''}} - 81 y = e^{9 x}

y = c_{1} e^{9 x} + c_{2} e^{- 9 x} + \frac{e ^{9 x} x}{18}

Solution steps

y^{''} (x) - 81 y = e^{9 x}

Solve linear ODE:

y = c_{1} e^{9 x} + c_{2} e^{- 9 x} + \frac{e ^{9 x} x}{18}

y = c_{1} e^{9 x} + c_{2} e^{- 9 x} + \frac{e ^{9 x} x}{18}

What is the solution for y^{''}-81y=e^{9x} ?
The solution for y^{''}-81y=e^{9x} is y=c_{1}e^{9x}+c_{2}e^{-9x}+(e^{9x}x)/(18)