What is the solution for t(dy)/(dt)=2te^t-y+6t^2 ?

The solution for t(dy)/(dt)=2te^t-y+6t^2 is y=(2(e^tt-e^t))/t+2t^2+(c_{1})/t

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t(dy)/(dt)=2te^t-y+6t^2

t \frac{d y}{d t} = 2 t e^{t} - y + 6 t^{2}

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

Solution steps

t \frac{d y}{d t} = 2 t e^{t} - y + 6 t^{2}

Solve linear ODE:

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

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

\int 2 e^{6} d x

\int 1 + x d x

x \to 8 lim (\frac{x}{x ^{2} - 64})

x \frac{d y}{d x} + y^{2} + y = 0

\frac{d}{d x} (9 x + x^{2})

What is the solution for t(dy)/(dt)=2te^t-y+6t^2 ?
The solution for t(dy)/(dt)=2te^t-y+6t^2 is y=(2(e^tt-e^t))/t+2t^2+(c_{1})/t