What is the solution for (dy)/(dt)+2/t y=t-1+y/t ?

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

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(dy)/(dt)+2/t y=t-1+y/t

\frac{d y}{d t} + \frac{2}{t} y = t - 1 + \frac{y}{t}

y = \frac{t ^{2}}{3} - \frac{t}{2} + \frac{c _{1}}{t}

Solution steps

\frac{d y}{d t} + \frac{2}{t} y = t - 1 + \frac{y}{t}

Solve linear ODE:

y = \frac{t ^{2}}{3} - \frac{t}{2} + \frac{c _{1}}{t}

y = \frac{t ^{2}}{3} - \frac{t}{2} + \frac{c _{1}}{t}

y = 9 x^{\frac{5}{2}} - 7 x^{\frac{3}{2}}, at x = 4

\frac{d y}{d x} - 2 (x + 1)^{3} = \frac{4}{( x + 1 )} y

f (x) = arctan (\frac{π}{x})

y^{^{'}} = 6 y^{2} sin (x)

\int \frac{1}{( 9 x - 1 ) ^{2}} d x

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