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}

x^{^{''}} - 4 x^{^{'}} + 3 x = 2 e^{t} - 5 e^{2 t}

y^{^{''}} + 4 y = t^{2} + 7 e^{t}, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} + y^{^{'}} = (3 t^{2} + 2 t) e^{t} + cos (\frac{t}{2})

y^{^{''}} + 5 y^{^{'}} - 6 y = 2 sin (4 x)

y^{^{'''}} + 3 y^{^{''}} - 9 y^{^{'}} + 5 y = 4 e^{- x} + cos (x)

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)