What is the solution for ((dy)/(dt))-(3/t)*y=2t^3e^{2t},y(1)=0 ?

The solution for ((dy)/(dt))-(3/t)*y=2t^3e^{2t},y(1)=0 is y=e^{2t}t^3-e^2t^3

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((dy)/(dt))-(3/t)*y=2t^3e^{2t},y(1)=0

(\frac{d y}{d t}) - (\frac{3}{t}) \cdot y = 2 t^{3} e^{2 t}, y (1) = 0

y = e^{2 t} t^{3} - e^{2} t^{3}

Solution steps

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

Solve linear ODE:

y = e^{2 t} t^{3} - e^{2} t^{3}

y = e^{2 t} t^{3} - e^{2} t^{3}

f (x) = 7 x^{2} + 6 x

- 2 x^{2}, at x = - 2

\frac{1}{x ^{2}}

\frac{12}{s ^{2} - 5}

1 - 4 x

What is the solution for ((dy)/(dt))-(3/t)*y=2t^3e^{2t},y(1)=0 ?
The solution for ((dy)/(dt))-(3/t)*y=2t^3e^{2t},y(1)=0 is y=e^{2t}t^3-e^2t^3