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

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- Solution b

Solution

The product rule gives

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.

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