What is the solution for y^{''}-16y^'+64y=5te^{8t} ?

The solution for y^{''}-16y^'+64y=5te^{8t} is y=c_{1}e^{8t}+c_{2}te^{8t}+(5e^{8t}t^3)/6

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y^{''}-16y^'+64y=5te^{8t}

y^{^{''}} - 16 y^{^{'}} + 64 y = 5 t e^{8 t}

y = c_{1} e^{8 t} + c_{2} t e^{8 t} + \frac{5 e ^{8 t} t ^{3}}{6}

Solution steps

y^{''} (t) - 16 y^{'} (t) + 64 y = 5 t e^{8 t}

Solve linear ODE:

y = c_{1} e^{8 t} + c_{2} t e^{8 t} + \frac{5 e ^{8 t} t ^{3}}{6}

y = c_{1} e^{8 t} + c_{2} t e^{8 t} + \frac{5 e ^{8 t} t ^{3}}{6}

2 y^{^{''}} - 3 y^{^{'}} = 9 x^{2} + 10

y^{^{''}} - y^{^{'}} - 2 y = sin (t)

x^{^{''}} + 14 x^{^{'}} + 98 x = 1960

y^{^{''}} + 4 y = sin (x), y (0) = 1, y^{^{'}} (0) = 2

x^{^{''}} + 4 x = 289 + e^{t} \cdot sin (2 t)

What is the solution for y^{''}-16y^'+64y=5te^{8t} ?
The solution for y^{''}-16y^'+64y=5te^{8t} is y=c_{1}e^{8t}+c_{2}te^{8t}+(5e^{8t}t^3)/6