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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. $(0, 10)$
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