What is the solution for x^{''}-8x^'+16x=4te^{4t} ?

The solution for x^{''}-8x^'+16x=4te^{4t} is x=c_{1}e^{4t}+c_{2}te^{4t}+(2e^{4t}t^3)/3

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x^{''}-8x^'+16x=4te^{4t}

x^{^{''}} - 8 x^{^{'}} + 16 x = 4 t e^{4 t}

x = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{2 e ^{4 t} t ^{3}}{3}

Solution steps

x^{''} (t) - 8 x^{'} (t) + 16 x = 4 t e^{4 t}

Solve linear ODE:

x = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{2 e ^{4 t} t ^{3}}{3}

x = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{2 e ^{4 t} t ^{3}}{3}

\int - cos (4 x) d x

\frac{d}{d x} (7^{x + a r c c o s (x)})

y^{^{''}} + 4 y^{^{'}} + 20 y = 0

\frac{\partial}{\partial x} (0.0099999)

\int 1 + 5 x^{4} (20 x^{3}) d x

What is the solution for x^{''}-8x^'+16x=4te^{4t} ?
The solution for x^{''}-8x^'+16x=4te^{4t} is x=c_{1}e^{4t}+c_{2}te^{4t}+(2e^{4t}t^3)/3