 Solution

ID: past-exam-of-the-algebra-1-and-differential-equations-1-course-of-the-university-of-oxford/2015/4/b/i/solution

Factor each component of the vector field. The horizontal-velocity nullclines and vertical-velocity nullclines are, respectively,

\overset{x}{˙} = 0 : x = 0, y = 1, x + y = 1; \overset{y}{˙} = 0 : y = 0, x y = 2.

The last curve is a hyperbola. In the nonnegative quadrant its branch is

y = 2/ x

for

x > 0

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