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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

0.5 y^{^{''}} + 5 y^{^{'}} + 12 y = e^{- 4 t} (4 t - 2)

y^{^{''}} + y^{^{'}} - 2 y = u π (t) - u^{2} π (t)

y^{^{''}} + 2 y^{^{'}} - 3 y = e^{2 t} - 2 t

x^{^{''}} + 36 x = 8 cos (6 t)

y^{^{''}} - 3 y^{^{'}} + 2 y = 7 x + 28

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