What is the solution for y^{''}-6y^'+9y=4te^{3t} ?

The solution for y^{''}-6y^'+9y=4te^{3t} is y=c_{1}e^{3t}+c_{2}te^{3t}+(2e^{3t}t^3)/3

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y^{''}-6y^'+9y=4te^{3t}

y^{^{''}} - 6 y^{^{'}} + 9 y = 4 t e^{3 t}

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

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = 4 t e^{3 t}

Solve linear ODE:

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

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

f (x) = ln (9 sin^{2} (x))

\int \frac{3 x - 1}{x ^{2} - 4} d x

- 3 (sin (4 (t - \frac{5 π}{4})))

\frac{\partial}{\partial x} (\frac{1}{7 + 5 x})

\int (x^{3} + 2)^{2} (3 x^{2}) d x

What is the solution for y^{''}-6y^'+9y=4te^{3t} ?
The solution for y^{''}-6y^'+9y=4te^{3t} is y=c_{1}e^{3t}+c_{2}te^{3t}+(2e^{3t}t^3)/3