 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2014/9/b/solution

e^{s i n x}

. Multiplying through gives

(y e^{s i n x})^{'} = 2 sin x cos x e^{s i n x} .

With

u = sin x

, the right side integrates to

2 e^{u} (u - 1)

. Consequently

y = 2 sin x - 2 + C e^{- s i n x} .

All coefficients are smooth, so these real solutions extend over the whole real axis.

 New to topics? Read the docs here!