What is the solution for y^{''}-8y^'+16y=t^{-2}e^{4t} ?

The solution for y^{''}-8y^'+16y=t^{-2}e^{4t} is y=c_{1}e^{4t}+c_{2}te^{4t}-e^{4t}ln(t)-e^{4t}

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y^{''}-8y^'+16y=t^{-2}e^{4t}

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 2} e^{4 t}

y = c_{1} e^{4 t} + c_{2} t e^{4 t} - e^{4 t} ln (t) - e^{4 t}

Solution steps

y^{''} (t) - 8 y^{'} (t) + 16 y = t^{- 2} e^{4 t}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} t e^{4 t} - e^{4 t} ln (t) - e^{4 t}

y = c_{1} e^{4 t} + c_{2} t e^{4 t} - e^{4 t} ln (t) - e^{4 t}

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

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\frac{d}{d x} (lo g_{\frac{1}{x}} (e))

\int \frac{1 + 3 x}{x} d x

\int csc^{4} (x) cot^{5} (x) d x

What is the solution for y^{''}-8y^'+16y=t^{-2}e^{4t} ?
The solution for y^{''}-8y^'+16y=t^{-2}e^{4t} is y=c_{1}e^{4t}+c_{2}te^{4t}-e^{4t}ln(t)-e^{4t}