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_{0}^{2 π} sin^{2} (t) d t

\frac{\partial}{\partial x} (25 x^{(\frac{3}{4})} y^{\frac{1}{4}})

y^{^{'}} + \frac{2 ( y - 1 )}{x} = 0

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

\int_{0}^{1} e^{2 x} d x

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