# GATE Papers >> EEE >> 2017 >> Question No 27

Question No. 27

Consider the different equation with $y(1)=2\mathrm\pi\;$. There exists a unique solution for the differential equation when $t$ belongs to the interval

Solution of Question No 27 of GATE 2017 EEE Paper

The differential equation can be reframed as

$\frac{\mathrm{dy}}{\mathrm{dt}}=\frac{\sin{\displaystyle\mathrm t}{\displaystyle-}{\displaystyle5}{\displaystyle\mathrm{ty}}}{(\mathrm t^2)-81}$

f (t, y) = $\frac{\sin{\displaystyle\mathrm t}{\displaystyle-}{\displaystyle5}{\displaystyle\mathrm{ty}}}{(\mathrm t^2-81)}$

$\frac{\mathrm{df}}{\mathrm{dy}}=\frac{-5\mathrm t}{\left(\mathrm t^2-81\right)}$

The function f and $\frac{\mathrm{df}}{\mathrm{dy}}$ are defined and continuous at all points expect t = 9 & t = – 9

So, solution is unique in an open interval around t = 1

Hence, only option A doesn't include either t = 9 or t = –9