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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 5 y^{^{'}} + 6 y = - 2 x + 1

0.05 y^{^{''}} + 5 y^{^{'}} + \frac{1}{0.006} y = 5 sin (25 x)

(d^{2} - d) y = e^{x} cos (x)

y^{^{''}} + 17 y^{^{'}} + 30 y = cos (2 t)

e^{x} y^{^{''}} + 2 e^{x} y^{^{'}} + 5 e^{x} y = sin (2 x)

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