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

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

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(dy)/(dt)= 2/t y+t^3e^t

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

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

Solution steps

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

Solve linear ODE:

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

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

\int 3^{- 6 x} d x

\frac{3}{s ( s ^{2} + 2 s + 4 )}

\int y^{- 5} d y

y^{^{'}} = y^{2} cos (x)

x \to - 1 lim ((x + 2 x^{5})^{3})

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