What is the solution for (dy)/(dt)-3/t y=2t^3e^{2t} ?

The solution for (dy)/(dt)-3/t y=2t^3e^{2t} is y=e^{2t}t^3+c_{1}t^3

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(dy)/(dt)-3/t y=2t^3e^{2t}

\frac{d y}{d t} - \frac{3}{t} y = 2 t^{3} e^{2 t}

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

Solution steps

\frac{d y}{d t} - \frac{3}{t} y = 2 t^{3} e^{2 t}

Solve linear ODE:

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

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

\frac{d}{d x} (x^{3} + 2 x^{2} - 4 x + 2)

k = 1 \sum \infty e^{- k}

x \to \infty lim (e^{x} - x)

3 v + \frac{d v}{d x} = 0

\int (4 + x^{8})^{5} 8 x^{7} d x

What is the solution for (dy)/(dt)-3/t y=2t^3e^{2t} ?
The solution for (dy)/(dt)-3/t y=2t^3e^{2t} is y=e^{2t}t^3+c_{1}t^3