$$
y'+\frac{2}{t} y = \frac{\sin t}{t} \\
\mu y' + \frac{2 \mu}{t} y = \mu \frac{\sin t}{t} \\
\mu = t^2 \\
\frac{d}{dt} t^2 y = t \sin t \\
t^2 y = \int t \sin t dt \\
y = \frac{\sin t - t \cos t + C}{t^2}
$$
use initial value
$$
1 = \frac{4\left(1 - 0 + C\right)}{\pi^2}\\
C= \frac{\pi^2-4}{4}\\
y = \frac{\sin t - t \cos t + \frac{\pi^2-4}{4}}{t^2}\\
y = \frac{4\sin t - 4t \cos t + \pi^2-4}{4t^2}
$$
