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Transcript of EMCF-18-F14
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8/9/2019 EMCF-18-F14
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MATH 3321 Quiz 18 11/19/14
1. The linear differential system equivalent to the differential equation
y 2y 8y= 2e3t
is:
(a)
x1x2
=
0 18 2
x1x2
+
0
2e3t
(b)
x1x2
=
0 18 2
x1x2
+
2e3t
0
(c)
x1x2
=
0 18 2
x1x2
+
0
2e3t
(d)
x1x2
=
0 18 2
x1x2
+
2e3t
0
(e) None of the above.
2. The linear differential system equivalent to the differential equation
y 4
ty +
6
t2y= 2t2
is:
(a)
x1x2
=
0 16/t2 4/t
x1x2
+
02t2
(b)
x1x2
=
0 16/t2 4/t
x1x2
+
2t2
0
(c)
x1x2
=
0 16/t2 4/t
x1x2
+
02t2
(d) x1x2
= 0 16/t
2
4/t x1
x2+ 2t
2
0
(e) None of the above.
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3. Find a fundamental set of solutions of x =
0 110 3
x. Hint: This system is equivalent
to a second order homogeneous equation.
(a) x1=
e5t
5e5t
, x2=
e2t
2e2t
(b) x1=
e5t
5e5t, x2=
e
2t
2e2t
(c) x1=
e5t
e5t
, x2=
e2t
e2t
(d) x1=
e5t
5e5t
, x2=
e2t
2e2t
(e) None of the above.
4. Find a fundamental set of solutions of x = 0 1
12/t
2
6/tx. Hint: This system is
equivalent to a second order homogeneous equation.
(a) x1=
t3
t2
, x2=
t4
t3
(b) x1=
t3
3t4
, x2=
t4
4t5
(c) x1=
t3
3t2
, x2=
t4
4t3
(d) x1= t3
3t2, x2=
t4
4t5
(e) None of the above.
5. The general solution of x =
0 16 1
x+
0
2e2t
is:
(a) x= C1e3t
13
+C2e2
t
12
+
0
1
2e2t
(b) x= C1e3t 1
3+C2e2t 1
2+
1
2e2t
e2t
(c) x= C1e3t
13
+C2e
2t
12
+
e2t
0
(d) x= C1e3t
13
+C2e
2t
12
+
e2t
2e2t
(e) None of the above.
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6. The general solution of x =
0 1 00 0 1
4 4 1
x is: Hint: This system is equivalent to a
third order homogeneous equation.
(a) x= C1e2t
124+C2e2t
12
4 +C3et
11
1
(b) x= C1e2t
12
4
+C2e2t
12
4
+C3et
11
1
(c) x= C1e2t
12
4
+C2e2t
12
4
+C3et
10
1
(d) x= C1e2t
12
4
+C2e2t
12
4
+C3et
11
1
(e) None of the above.
7. A fundamental set of solutions of x =
3 2
1 2
x is:
(a) x1= e4t
21
, x2= e
t
11
(b) x1= e4t
21
, x2= e
t
11
(c) x1= e4t
21
, x2= e
t
11
(d) x1= e4t
21
, x2= e
t
11
(e) None of the above.
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8. The solution of the initial-value problem x =
1 1
4 2
x, x(0) =
2
5
is:
(a) x= 35e3t
14
+ 13
5e2t
11
(b) x=
3
5e3t 1
4 13
5e2t 1
1
(c) x= 35e3t
1
4
13
5e2t
11
(d) x= 35e3t
14
13
5e2t
11
(e) None of the above.
9. A fundamental set of solutions of x =
3 2 23 1 3
1 2 0
x is:
(a) x1= e2t
011
, x2= et
11
1
, x3= et
101
(b) x1= e2t
10
1
, x2=et
11
1
, x3= et
12
1
(c) x1= e2t
02
1
, x2= et
11
3
, x3= et
10
1
(d) x1= e2t
01
1
, x2=et
11
1
, x3=et
10
1
(e) None of the above.
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10. The general solution of x =
1 3 11 1 1
3 3 1
x is
(a) x= C1e2t
3
2
3
+C2 e2
t
11
1
+C3e
t
31
3
(b) x= C1e
2t
32
3
+C2 e2t
10
1
+C3et
31
3
(c) x= C1e2t
323
+C2 e2t
10
1
+C3et
313
(d) x= C1e2t
32
3
+C2 e
2t
1
10
+C3e
t
3
13
(e) None of the above.
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