What is the solution for y^{''}-16y^'+64y=t^{-2}e^{8t} ?

The solution for y^{''}-16y^'+64y=t^{-2}e^{8t} is y=c_{1}e^{8t}+c_{2}te^{8t}-e^{8t}ln(t)-e^{8t}

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y^{''}-16y^'+64y=t^{-2}e^{8t}

y^{^{''}} - 16 y^{^{'}} + 64 y = t^{- 2} e^{8 t}

y = c_{1} e^{8 t} + c_{2} t e^{8 t} - e^{8 t} ln (t) - e^{8 t}

Solution steps

y^{''} (t) - 16 y^{'} (t) + 64 y = t^{- 2} e^{8 t}

Solve linear ODE:

y = c_{1} e^{8 t} + c_{2} t e^{8 t} - e^{8 t} ln (t) - e^{8 t}

y = c_{1} e^{8 t} + c_{2} t e^{8 t} - e^{8 t} ln (t) - e^{8 t}

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f (x) = 5 x + 75, at x = 5

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\int \frac{1}{( 1 + x ^{2} )} d x

What is the solution for y^{''}-16y^'+64y=t^{-2}e^{8t} ?
The solution for y^{''}-16y^'+64y=t^{-2}e^{8t} is y=c_{1}e^{8t}+c_{2}te^{8t}-e^{8t}ln(t)-e^{8t}