Verify that the given vector is the general solution of the corresponding homogeneous system, and then solve the nonhomogeneous system. Assume that t>0. 24 -16-2ttx' =x+16 -16-1-7x(©)= C1-8 + c2t16(s)1+297168.18 + c22.1t -2316-731x = C1162532116252+135 \ 1617t -116x = C11-8+ c2z1629731()(*).(;).(;)8125171-81-2549x = c1+ c216135-16697116252171-161-2549x = c118 + c21699135-16697´ 17135 \ 16.-1621´ 16162529723 \ 31.

tx'=24-1616-16x+-2tt25-t-7xc=c112t-8+c121t16

Math

Advanced Math

24 -16 -2t tx' 16 -16) *+ (25 ()- (;)*. x(C) = C1 + c2 p16. 1

24 -16 -2t tx' 16 -16) + (25 ()- (;). x(C) = C1 + c2 p16. 1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Verify that the given vector is the general solution of the corresponding homogeneous system, and then solve the nonhomogeneous system. Assume that t>0.

24 -16
-2t
tx' =
x+
16 -16
-1-7
x(©)
= C1
-8 + c2
t16
(s)
1
+
297
16
8.
18 + c2
2.
1
t -
23
16
-7
31
x = C1
16
25
3
2
1
16
25
2
+
135 \ 16
17
t -
1
16
x = C1
1-8
+ c2
z16
297
31
()
(*).
(;).
(;)
8
125
17
1
-8
1-25
49
x = c1
+ c2
16
135
-16
697
1
16
25
2
17
1
-16
1-25
49
x = c1
18 + c2
16
99
135
-16
697
´ 17
135 \ 16.
-16
2
1
´ 16
16
25
297
23 \ 31.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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