 Solution

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

u = x + y

turns the equation into

u^{'} = 1 + u^{2}

. Separating and integrating gives

arctan u = x + C

, hence

y = tan (x + C) - x .

Each real solution is defined on an interval containing no pole of the tangent. There is no real constant-

u

solution discarded by division, since

1 + u^{2} > 0

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