9.Match the differential equation with the direction field:

  

a dy/dx = x+y

b dy/dx = x2

 

c dy/dx = -y

 

d dy/dx = y

 

 

 

I

 

II

III

IV

 

Solution

The solution curves of the graph in I are similar to a cubic polynomial, soI corresponds to b. The direction fields in II have the vectors pointing up for y > 0 horizontal for y = 0, and downward for y < 0; so II corresponds to d. By a simialar argument, Iv corresponds to c. Finally, by elimination,III corresponds to a