72 Ordinary Differential Equations
- y' = y/(x -1) +x^2 ; y(O) = 1
- y' = y/x + sinx^2 ; y(-1) = -1
1- y(l) = 2
- y' = (cotx)y + sinx; y(7r/2) = 0
- A thermometer reading 70° F is taken outside where the temperature is
10° F. Five minutes later the thermometer reads 40° F. How long after
being taken outside is the thermometer reading within one-half a degree
of the outside temperature? - A thermometer reading 80° F is taken outside. Five minutes later the
thermometer reads 60° F. After another 5 minutes the thermometer
reads 50° F. What is the temperature outside? - At 1:00 p.m. a thermometer reading 10 ° F is removed from a freezer
and placed in a room whose temperature is 65° F. At 1:05 p.m. the
thermometer reads 25° F. Later the thermometer is placed back in the
freezer. At 1:30 p.m. the thermometer reads 32° F. When was the
thermometer returned to the freezer and what was the thermometer
reading at that time? - A invited B for morning coffee. A poured two cups of coffee. B added
enough cream to lower the temperature of his coffee 1° F. After 5 min-
utes A added enough cream to his coffee to lower the temperature 1° F
and both A and B began to drink their coffee. Who had the cooler
coffee?
In exercises 1 2- 17 use any technique to solve t h e given differentia l
equation.
- xdx -ydy = 0
13. ydx - xdy = 0
- (x^2 - y) dx + x dy = 0
15. xy(l - y) dx - 2 dy = 0
16. x(l - y^3 ) dx - 3y^2 dy = 0
- y(2x - 1) dx + x(x + 1) dy = 0