What is the solution for y^{''}-18y^'+81y=t^{-2}e^{9t} ?

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

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y^{''}-18y^'+81y=t^{-2}e^{9t}

y^{^{''}} - 18 y^{^{'}} + 81 y = t^{- 2} e^{9 t}

y = c_{1} e^{9 t} + c_{2} t e^{9 t} - e^{9 t} ln (t) - e^{9 t}

Solution steps

y^{''} (t) - 18 y^{'} (t) + 81 y = t^{- 2} e^{9 t}

Solve linear ODE:

y = c_{1} e^{9 t} + c_{2} t e^{9 t} - e^{9 t} ln (t) - e^{9 t}

y = c_{1} e^{9 t} + c_{2} t e^{9 t} - e^{9 t} ln (t) - e^{9 t}

x \to 1 lim (x^{2} + 3 - 2)

\frac{d}{d x} (\frac{5 ^{x}}{cos ( x )})

x \to 5 lim (3 x - 7)

y = x^{4} - 4 x^{2}, y = x^{2} - 4

y^{^{'}} = \frac{x ^{4}}{16} (e^{- y})

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