3 parts, 9 problems due Monday, February 2nd, 4pm, in box in Math Department Main Office, 244 Mathematics Building
Part A
1.1: 17, 18, 19, 20
Instructions: in each of these four problems, a differential equation, its general solution, and an initial condition are given.
**NEW** special note for problem #20:
For problem 20, you can change the initial condition from y(0)=10 to y(0)=2 to make it easier to draw the curve on to of the slope field. You don't have to make a change if you have already completed the problem, just make sure the solution in (a) is consistent with the curve for (c) and clearly indicate which initial condition you used.
(a) Find the particular solution fulfilling the given initial condition.
(b) Sketch a slope field for the differential equation, following these tips:
- For 17-19, determine where dy/dx = 0. Sketch slope lines on at least five of these points. In the same manner, locate and sketch slope lines where dy/dx = 1, -1, 2, and -2.
- For 20, what is dy/dx along the line y=x? Sketch slope lines on at least five points along this line. Do the same along lines y=x+1, y=x-1, y=x+2, and y=x-2. (In general, notice: what is dy/dx when y=x+b?)
(c) Sketch the solution curve for your answer to (a) on top of your slope field.
(d) Determine if the differential equation can be solved using Separation of Variables. If so, derive the general solution. If not, write "NOT SEPARABLE."
Part B
1.4: 3, 8, 9, 15, 18
Instructions: same as in textbook.
Part C
On top of first page,
1) Write "Priority: __" and in the blank, indicate the problem for which you want the most detailed feedback (for example, "Priority: 1.1.17")
On back of last page, please answer the following poll:
2) I obtained this homework from (UB) UBlearns, or (JM) Instructor website, or (O) other, and
3) I prefer to obtain homework assignments from (UB) UBlearns, or (JM) Instructor website, or (O) other