Question

In each of Problems 1 through 4 draw a direction field for the given differential equations. Based on the direction field, determine the behavior of y as t → +∞. If this behavior depends on the initial value of y at t = 0, describe this dependency.

1. y ' = 3 + 2y

2. y ' = 3 − 2y

3. y ' = −y(5 − y)

4. y ' = y(y − 2)2

Answer 1

④ y a 3+27 y-29=3 this is the first-order ode. . If= ě 2* gert eztakte Yezz - 2 / 2 + cet as tas too y(t) ② Y= 3-24 I J'+2y=3 I similarly as done above we can obtain the sot Ifa et get = feet dit te J (+)2 3 + cezt too , y It) 3 which is of the fixed point of the as tas too, y It) 2 above first order ode. similarle Merly we can proceed the for the 83 an a shown the direction field for Q.3 and 8.4.

Q.1 st

0.2 5

Q.3 5 -

Q.4 -5