What is the solution for x^{''}-16x^'+64x=3te^{8t} ?

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

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x^{''}-16x^'+64x=3te^{8t}

x^{^{''}} - 16 x^{^{'}} + 64 x = 3 t e^{8 t}

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

Solution steps

x^{''} (t) - 16 x^{'} (t) + 64 x = 3 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}}{2}

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

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