M 408S
Worksheet: Separable differential equations
Work your problems on a separate sheet of paper.
1. Find the general solution to each differential equation.
(a)
(b)
dy
dx
dy
dt
= xe−y
= 10 − 2y
(c) (y 2 + xy 2 )y 0 = 1
2. Find the general and particular solutions to each differential equation.
(b)
du
dt
dy
dx
(c)
dy
dx
(a)
=
2t+sec2 t
,
2u
=
ln x
,
xy
u(0) = −5
y(1) = 2
p
= 2x 1 − y 2 , y(0) = 0
3. For problem 2 (c), is there more than one particular solution? If the initial value had
been y(0) = 2, what would have happened?
4. Suppose a population grows according to a logistical model with initial population
1000 and carrying capacity 10,000. If the population grows to 2,500 after one year,
what will the population be after another three years?
1