MATH 336 Extra Review Questions for Exam 1
1. Determine the solution of the initial value problem
dx =xy3+ 3x2y3, y(1) = 1/2
2. Determine the particular solution of the initial value problem
dx = 1 + x+y, y(1) = 4
3. Find the general solution of the diﬀerential equation
4. Find the solution of dy
dx = 2x√y−2y
5. Determine the value of the constant bso that the following DE is exact. Then ﬁnd the
general solution with this value of b.
(xexy +ex+bx2y2+ 1)dy
dx + (yexy +yex+ 2xy3) = 0
6. A turkey with initial temperature 40◦F is placed into an oven with constant temperature of
350◦F. After 2 hours, the temperature of the turkey is 80◦F. Assume that the temperature
of the turkey obeys Newton’s law of heating: the rate of change in the temperature is
proportional to the diﬀerence between the temperature and the ambient temperature.
Set up and solve a diﬀerential equation to determine when the temperature of the turkey
will be 160◦F.
7. A tank initially contains 10 gal of pure water. Brine containing 4 lb of salt per gallon enters
the tank at 2 gal/min, and the (perfectly mixed) solution leaves the tank at 3 gal/min.
Let x(t) denote the amount of salt in the tank at time t.
Set up and solve the appropriate initial value problem to explicitly determine the function
8. In a population of 100 people, let P(t) be the number of people who have heard a certain
rumor by day t. Assume that the rumor spreads at a rate proportional to the product
of the number of people who have heard it and the number of people who have not yet
heard it. Further assume that P(0) = 10 and P′(0) = 3. Set up and solve the initial-value
problem to determine P(t).
Answers on back of this sheet.
Note: These old exam questions are provided in case they help you in studying for the exam.
However, our exam may be quite diﬀerent, so you should not use this as your only study
Extra review questions for exam 1: determine the solution of the initial value problem dy dx. = xy3 + 3x2y3, y(1) = 1/2: determine the particular solution of the initial value problem x dy dx. = 1 + x + y, y(1) = 4: find the general solution of the di erential equation, find the solution of x(x + y) dy dx. = 2x y 2y: determine the value of the constant b so that the following de is exact. Then nd the general solution with this value of b. (xexy + ex + bx2y2 + 1) dy dx. + (yexy + yex + 2xy3) = 0: a turkey with initial temperature 40 f is placed into an oven with constant temperature of. Set up and solve a di erential equation to determine when the temperature of the turkey will be 160 f: a tank initially contains 10 gal of pure water.