What is the solution for y^{''}-5y^'-36y=e^{9x} ?

The solution for y^{''}-5y^'-36y=e^{9x} is y=c_{1}e^{9x}+c_{2}e^{-4x}+(e^{9x}x)/(13)

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y^{''}-5y^'-36y=e^{9x}

y^{^{''}} - 5 y^{^{'}} - 36 y = e^{9 x}

y = c_{1} e^{9 x} + c_{2} e^{- 4 x} + \frac{e ^{9 x} x}{13}

Solution steps

y^{''} (x) - 5 y^{'} (x) - 36 y = e^{9 x}

Solve linear ODE:

y = c_{1} e^{9 x} + c_{2} e^{- 4 x} + \frac{e ^{9 x} x}{13}

y = c_{1} e^{9 x} + c_{2} e^{- 4 x} + \frac{e ^{9 x} x}{13}

y^{^{''}} + y^{^{'}} + y = sin (x) + x + x^{2} - 1

y^{^{''}} + y = e^{2 x}, y (0) = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = x e^{- x}

x^{^{''}} + x = 2 e^{t}

y^{^{'''}} - 3 y^{^{''}} + 4 y = 12 e^{2 x} + 4 e^{3 x}

What is the solution for y^{''}-5y^'-36y=e^{9x} ?
The solution for y^{''}-5y^'-36y=e^{9x} is y=c_{1}e^{9x}+c_{2}e^{-4x}+(e^{9x}x)/(13)