What is the solution for y^{''}-18y^'+81y=t^9e^{9t} ?

The solution for y^{''}-18y^'+81y=t^9e^{9t} is y=c_{1}e^{9t}+c_{2}te^{9t}+(e^{9t}t^{11})/(110)

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y^{''}-18y^'+81y=t^9e^{9t}

y^{^{''}} - 18 y^{^{'}} + 81 y = t^{9} e^{9 t}

y = c_{1} e^{9 t} + c_{2} t e^{9 t} + \frac{e ^{9 t} t ^{11}}{110}

Solution steps

y^{''} (t) - 18 y^{'} (t) + 81 y = t^{9} e^{9 t}

Solve linear ODE:

y = c_{1} e^{9 t} + c_{2} t e^{9 t} + \frac{e ^{9 t} t ^{11}}{110}

y = c_{1} e^{9 t} + c_{2} t e^{9 t} + \frac{e ^{9 t} t ^{11}}{110}

y^{^{''}} - y^{^{'}} = 3 - 4 x, y (0) = - 3, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x} \cdot ln (x)

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

y^{^{''}} + 25 y = x^{2}

y^{^{''}} - 2 y^{^{'}} + y = e^{- x} ln (x)

What is the solution for y^{''}-18y^'+81y=t^9e^{9t} ?
The solution for y^{''}-18y^'+81y=t^9e^{9t} is y=c_{1}e^{9t}+c_{2}te^{9t}+(e^{9t}t^{11})/(110)