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

The solution for (dy)/(dt)-(3/t)*y=2t^3*e^{(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}) \cdot y = 2 t^{3} \cdot e^{(2 t)}

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

Solution steps

\frac{d y}{d t} - (\frac{3}{t}) \cdot y = 2 t^{3} \cdot 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 t} (5 e^{- 2 t} + 3 t e^{- 2 t} - 2)

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (1) = 0, y^{^{'}} (1) = 4

x cos (x)

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

f (x) = ln (x - 1)

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