Math 182                                                         Name:                          Key                                                     

Quiz 4                                                             

 

All questions relate to the differential equation: 

1.  a.  The direction field for this differential equation is shown.  Sketch the solution curves that go through the points (0, 0)  and  (0, 1)  

       (Sketch as much of the solutions as is

       possible on the field in both directions)

 

   b.  Use either the differential equation itself or the direction field to determine:  Are there any equilibrium solutions?  Briefly justify your answer.

 

No, there are no equilibrium solutions.  These are solutions of the form y=constant, and we can see there are no horizontal solutions.  Alternatively, looking at the differential equation, we’d need to find a value of y for which dy/dx is always 0, and no such value exists.

 

 

 

 

 

   c.  For this differential equation with initial condition (1,0), use Euler’s Method, with step size ˝,  to approximate y when x=2.

(While you may use your calculator program to check your calculations, you should show all work so that I can see how you arrive at your values without needing the program)

 

x

y

y' = y-x

dx

dy

1

0

-1

.5

-.5

1.5

-.5

-2

.5

-1

2

-1.5

 

 

 

 

 

2.   Find the general solution to the separable differential equation