MATH 1920 - CHAPTER 7 PRACTICE
1. Determine if is a solution of the third order differential equation:yCx
=
3
x y x y xy y
3 2 3 3 0
′′′ +′′ −′− =
2. BONUS: Prove that is a solution of the first order differential equation: y x xy C
2 2
− − =
( )x y y x y
−′+ + =
2 2 0
3. #8 on page 508; use c = 1, 2, 3 for part c)
4. #12 on page 513
5. Solve the differential equation: [solve answer for y]
x y yx y
2 2
′− =
6. Solve the differential equation: [do not solve answer for y]x y dy
dx xcos sec
20
− =
7. Find the particular solution of the differential equation that satisfies the given condition:
and y = 4 when x = 9 [solve answer for y]
xy y x y
′− =
8. A curve passes through (3, 10) and has the property that the slope of the curve at every point P
is the square of the x-coordinate of P. What is the equation of the curve?
9. A curve passes through (0, 3) and has the property that the slope of the curve at every point P
is the product of the coordinates of P. What is the equation of the curve?
Refer to #13 on page 533 for a discussion of Newton’s Law of Cooling. See solution to #14 on my web
site for one method of solution.
10. On a hot day in Phoenix the temperature may reach . On such a day an outdoor120oF
thermometer is taken inside a grocery where the temperature is 68oF.
a) If the thermometer reads after one minute, what will the reading be after two more 100oF
minutes?
b) When will the thermometer read 70
o
F?
11. The temperature within a food freezer is and the room temperature is a constant
−
16oC20oC.
At 11 PM the power goes off, and at 6 AM the next morning the temperature in the freezer has
risen to At what time will the temperature in the freezer reach the critical value of if
−
10oC.0oC
the power remains off and the freezer is not opened?