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Differential Equations

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A Tougher Initial Value Problem

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The solution of the initial value problem:

$$\begin{equation} t y' + (t+2)y = t, y(1) = 0, t>0 \end{equation}$$

...is:

A

$y(t) = 1-\cfrac{2}{t} + \cfrac{2}{t^2} - \cfrac{\exp(1-t)}{t^2}$

B

$y(t) = -1-\cfrac{2}{t} + \cfrac{2}{t^2} + \cfrac{\exp(1-t)}{t^2}$

C

$y(t) = 1-\cfrac{2}{t} + \cfrac{2}{t^2} - \cfrac{\exp(-t)}{t^2}$

D

None of the above