Past exam of the mathematical methods II course of the University of Oxford / 2016 resit / 1 / b

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- Solution b

Solution

Implicit differentiation gives

2 y^{'} = 15 x^{2} + (cos y) y^{'}

. Therefore

y^{'} = \frac{15 x ^{2}}{2 - cos y} .

For real

y

, the denominator is at least one, so division introduces no singularity. In fact the function

2 y - sin y

is strictly increasing, consistent with a unique real branch

y (x)

.

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