Homework Equation Worksheet
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1
2Math 20820: Homework 11 – Part 2
Due Friday, Apr. 15.
1 2
1
1. Verify that
=
and
=
are both solutions to the second order linear
1
2
ODE
2
2
+ 3
= 0
2. For each equation determine the values of
for which the given differential
equation has solutions of the form
=
.
(a)
3 = 0
(b)
= 0
(c)
+
6 = 0
(d)
3
+ 2 = 0.
3. For the following differential equations determine whether they are linear, sepa-
rable, neither or both.
2
(a)
+
= 0
2
(b) (sin )
=
2
2
+
+
(c)
=
2
(d)
=
4
4. Let
2
=
with
(1) = 0
(a) Find the general solution to the differential equation.
(b) Find the solution to the initial value problem.
(c) What is the interval in which this solution exists?
(d) What is the behavior of this solution as
.
5. Let
2
= (1
2 )
with
(0) =
1 6
(a) Find the general solution to the differential equation writing
explicitly in
terms of .
(b) Find the solution to the initial value problem.
(c) What is the interval in which this solution is defined?
6. Let
2
3
=
with
(0) = 1
2
5
(a) Find the general solution to the differential equation writing
explicitly in
terms of .
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