 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-1/17/b/solution

d (y sin^{2} x) = y sin (2 x) d x + sin^{2} x d y .

Thus this is an exact differential, and its zero level differential means

y sin^{2} x = C

. The initial data set

C = 1

y = csc^{2} x, 0 < x < π .

The displayed interval is the maximal connected real interval containing

π /2

on which this finite-valued solution is defined.

 New to topics? Read the docs here!