Homework for §1.4
Find general solutions (implicit if necessary, explicit if convenient) of the differential
equations below. Primes denote derivatives with respect to x.
dy
+ 2xy 2 = 0
dx
dy
2. (1 − x2 )
= 2y
dx
dy
3. y 3
= (y 4 + 1) cos x
dx
.............................................................................
1.
Find an explicit particular solution to the initial value problems below.
π π
dy
= y, y
=
4. (tan x)
dx
2
2
dy
5.
= 6e2x−y , y(0) = 0
dx
.............................................................................
6. Suppose that you discover in your attic an overdue library book on which your
grandfather owed a fine of 30 cents 100 years ago. If an overdue fine grows exponentially at a 5% annual rate compounded continuously, how much would you have to
pay if you returned the book today?
7. A cake is removed from the oven at 210◦ F and left to cool at room temperature,
which is 70◦ F . After 30 minutes the temperature of the cake is 140◦ F . When will it
be 100◦ F ?