 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/14/a/ii/solution

For

a = 1

, integrate

Q = 2 x y sin x

with respect to

y

to obtain

f (x, y) = x y^{2} sin x + C (x) .

f_{x} = y^{2} sin x + x y^{2} cos x + C^{'} (x)

. Comparing with

P

gives

C^{'} (x) = 0

. Thus the most general potential on the plane is

f (x, y) = x y^{2} sin x + C, C \in R .

 New to topics? Read the docs here!