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

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

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t*(dy)/(dt)+y=2te^t

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

y = \frac{2 ( e ^{t} t - e ^{t} )}{t} + \frac{c _{1}}{t}

Solution steps

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

Solve linear ODE:

y = \frac{2 ( e ^{t} t - e ^{t} )}{t} + \frac{c _{1}}{t}

y = \frac{2 ( e ^{t} t - e ^{t} )}{t} + \frac{c _{1}}{t}

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