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Homework 1
Due 24 August 2010
Each question is worth 10 points
1.)
Given the differential equation:
t
ft
()
d
d
Af t
⋅
+
Be
C
−
t
⋅
⋅
=
Solve for
f(t)
given the initial condition that
f(0) = D
.
2.)
Consider the system of coupled differential equations:
t
f
d
d
Af
⋅
Bg
⋅
+
=
and
t
g
d
d
Cf
⋅
Dg
⋅
−
=
What are the characteristic roots (i.e.
. the eigenvalues) for this system of
equations?
3.)
Consider the equation:
π
x
⋅
log 4
e
x
e
1
2
=
Solve for x.
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View Full Document 4.)
Solve the following linear boundary value problem for
Φ
.
Make sure that you find
ALL possible solutions:
Φ
1
−
() 0
=
2
x
Φ
d
d
2
Φ
+
0
=
Φ
1
=
Solve the following linear boundary value problem for
Φ
.
Make sure that you find
ALL possible solutions:
Φπ
−
()0
=
2
x
Φ
d
d
2
Φ
+
0
=
=
Say something about the difference between these two cases
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This note was uploaded on 02/03/2011 for the course NE 301 taught by Professor Smith during the Spring '11 term at UNC.
 Spring '11
 smith

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