Answer
$y = -t~cos~t - t~~$ is a solution.
Work Step by Step
We can verify that $~~y = -t~cos~t - t~~$ is a solution:
$t \frac{dy}{dt} = (t)(t~sin~t-cos~t-1)$
$t \frac{dy}{dt} = (t^2~sin~t-t~cos~t-t)$
$t \frac{dy}{dt} = y+t^2~sin~t$
We can verify the initial condition:
$y(\pi) = (-\pi)~cos~(\pi) - (\pi)$
$y(\pi) = (-\pi)~(-1) - (\pi)$
$y(\pi) = \pi - \pi$
$y(\pi) = 0$
$y = -t~cos~t - t~~$ is a solution.
