Homework #1 Math 527
Instructions:
Solve the following problems, simplifying the solution as much as you can.
Use loose-leaf paper, not pages torn out from a spiral notebook.
Staple the pages together in the upper left-hand corner.
Write your name, Math 527, section #, HW 1 in the upper-right corner of the 1st page.
Your work, name, and section number must be legible and organized!
Solve the differential equation using separation of variables. For #4 solve the initial value
problem.
1.
dy
dt = (1 + t)(1 + y)
2.
dy
dt = 1 − t + y
2 − ty2
3.
dy
dx = e
x+y+3
4.
dy
dt =
2t
y + yt2
, y(2) = 3
Solve the 1st-order linear differential equation using an integrating factor. For #8 solve the
initial value problem.
5.
dy
dt + y cost = 0
6.
dy
dx +
2xy
1 + x
2
=
1
1 + x
2
7. (1 + t
2
)
dy
dt + ty = (1 + t
2
)
5/2
8.
dy
dx − 2xy = x, y(0) = 1
Find all solutions of the differential equation, both a family of solutions parameterized by an
arbitrary constant and a singular solution.
9.
dy
dx = x
p
1 − y
2
These problems are taken from M. Braun “Differential Equations and Their Applications,”
Springer-Verlag Applied Mathematical Sciences series, volume 15, 1975.
