Di¤erential Equations and Matrix Algebra I (MA 221), Fall Quarter, 1999-2000
Quiz 10 – Thursday, October 21, 1999
Box
NAME
12 pts 1. Circle the correct answer.
dx
The solution to
= 3t2 is
dt
a) x = t3
b) x = t3 + c
The solution to
a) x = ce7t
c) x = 6t + c
dx
= 7x; x(0) = 4 is
dt
b) x = 7e7t
c) x = 4e7t
dx
+ 2x = 4 is
dt
a) x = 2 + 2e¡2t
b) x = 2 + ce2t
d) x = cet
e) none of these
d) x = 7x2
e) none of these
d) x = e¡2t + c
e) none of these
The solution to
The solution to
a) x = ce¡3t
The solution to
a) x = t2 ¡ 3
The solution to
a) x = 1
c) x = 2 + ce¡2t
dx
= ¡3x; x(1) = 2 is
dt
b) x = 2e¡3t
c) x = e3 e¡3t
1
dx
= 2tx2 ; x(2) = ¡ is
dt
3
1
1
b) x = 2
c) x =
+c
t ¡1
t¡1
dx
= 3x(4 ¡ x2 ); x(0) = 2 is
dt
b) x = 2e¡2t
c) x = 2
d) x = 2e3 e¡3t
d) x =
1
1 ¡ t2
d) x = 2e¡t
e) none of these
e) none of these
e) none of these
12 pts 2. Circle the appropriate adjectives for the following DEs. Note: if you circle non-linear, then
you need not consider part c.
dx
= ¡2x
dt
a) …rst order = second order b) linear = non-linear c) homogeneous = non-homogeneous
dx
= 3x ¡ 6
dt
a) …rst order = second order
b) linear = non-linear
c) homogeneous = non-homogeneous
dx
= 3x2 + 3
dt
a) …rst order = second order
b) linear = non-linear
c) homogeneous = non-homogeneous
d2 x
2t dx
¡
e
¡ 3t3 x = 3t
2
dt
dt
a) …rst order = second order
b) linear = non-linear
c) homogeneous = non-homogeneous
d2 x
dx
¡x
=8
2
dt
dt
a) …rst order = second order
b) linear = non-linear
c) homogeneous = non-homogeneous
d2 x
= 5x
dt2
a) …rst order = second order
b) linear = non-linear
c) homogeneous = non-homogeneous
t
5 pts 3. Give the solution to
dx
= ¡2x; x(0) = 4:
dt
5 pts 4. Give the solution to
dx
= ¡3x + 6; x(0) = 7:
dt
2 pts 5. Are the functions e2t and 5e2t linearly dependent or linearly independent?
2 pts 6. Are the functions sin(2t) and 6 cos(2t) linearly dependent or linearly independent?
5 pts 7. State the Principle of Superposition for the second order, linear, homogeneous di¤erential
equation y 00 + p(x)y 0 + q(x)y = 0.