Consider the differential equation $(t^{2}-81)\frac{dy}{dt}+5t y=\sin(t)$ with $y(1)=2 \pi$. There exists a unique solution for this differential equation when $t$ belongs to the interval

1. $(-2, 2)$
2. $(-10, 10)$
3. $(-10, 2)$
4. $(0, 10)$