What is the solution for x^{''}-6x^'+9x=5te^{3t} ?

The solution for x^{''}-6x^'+9x=5te^{3t} is x=c_{1}e^{3t}+c_{2}te^{3t}+(5e^{3t}t^3)/6

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x^{''}-6x^'+9x=5te^{3t}

x^{^{''}} - 6 x^{^{'}} + 9 x = 5 t e^{3 t}

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

Solution steps

x^{''} (t) - 6 x^{'} (t) + 9 x = 5 t e^{3 t}

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} + y = - e^{3 x} + e^{2 x}

y^{^{''}} - 3 y^{^{'}} + 7 y = t^{2} + cos (t)

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

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = 4 cos (x)

(d^{3} + d) y = 6 x (2 x + 1)

What is the solution for x^{''}-6x^'+9x=5te^{3t} ?
The solution for x^{''}-6x^'+9x=5te^{3t} is x=c_{1}e^{3t}+c_{2}te^{3t}+(5e^{3t}t^3)/6