What is the solution for y^{''}-16y^'+64y=8t^6e^{8t} ?

The solution for y^{''}-16y^'+64y=8t^6e^{8t} is y=c_{1}e^{8t}+c_{2}te^{8t}+(e^{8t}t^8)/7

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y^{''}-16y^'+64y=8t^6e^{8t}

y^{^{''}} - 16 y^{^{'}} + 64 y = 8 t^{6} e^{8 t}

y = c_{1} e^{8 t} + c_{2} t e^{8 t} + \frac{e ^{8 t} t ^{8}}{7}

Solution steps

y^{''} (t) - 16 y^{'} (t) + 64 y = 8 t^{6} e^{8 t}

Solve linear ODE:

y = c_{1} e^{8 t} + c_{2} t e^{8 t} + \frac{e ^{8 t} t ^{8}}{7}

y = c_{1} e^{8 t} + c_{2} t e^{8 t} + \frac{e ^{8 t} t ^{8}}{7}

\frac{d}{d x} (x^{2} + 17)

\frac{d}{d x} (2 ln (x) + 3)

\int (x^{20} - 5 x^{4})^{5} (x^{19} - x^{3}) d x

\int \frac{3 x + 27}{( 2 x - 2 ) ( x + 5 )} d x

y = \frac{2}{x}, y = \frac{1}{2} x, y = 8 x

What is the solution for y^{''}-16y^'+64y=8t^6e^{8t} ?
The solution for y^{''}-16y^'+64y=8t^6e^{8t} is y=c_{1}e^{8t}+c_{2}te^{8t}+(e^{8t}t^8)/7