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

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

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

t \frac{d y}{d t} + (t + 1) y = t

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

Solution steps

t \frac{d y}{d t} + (t + 1) y = t

Solve linear ODE:

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

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

\frac{d}{d x} (x^{6} - 4 x^{5} + 5 x^{4} - 5 x^{2} + 4 x - 1)

\int_{1}^{5} 4 r^{2} ln (r) d r

f (x) = \frac{x}{x ^{2} - x}

\int (x^{3} - 6 x - 9) d x

f (x) = \frac{4 x}{( x - 9 ) ^{5}}

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