Choose the differential equation corresponding to this direction field. Select the correct answer.

A) $y ^ { t } = y + x y$
B) $y ^ { t } = \sin x \sin y$
C) $y ^ { t } = 2 - y$
D) $y ^ { t } = x + y - 1$
E) $y ^ { t } = x ( 2 - y )$

Question

Choose the differential equation corresponding to this direction field. Select the correct answer.

A) $y ^ { t } = y + x y$ 
B) $y ^ { t } = \sin x \sin y$ 
C) $y ^ { t } = 2 - y$ 
D) $y ^ { t } = x + y - 1$ 
E) $y ^ { t } = x ( 2 - y )$

Quizplus · Accepted Answer

The direction field shows that the slope of the solution curve is positive when y is less than 2 and negative when y is greater than 2. This suggests that the differential equation is of the form $y ^ { t } = x ( 2 - y )$, which has slope 0 when y=0 and slope -2 when y=2. Therefore, the correct answer is E.

Choose the Differential Equation Corresponding to This Direction Field yt=y+xyy ^ { t } = y + x yyt=y+xy

Choose the Differential Equation Corresponding to This Direction Field $y ^ { t } = y + x y$