Need help for #23 al Equations1X; X1 = e2t]**=23. x'5.-34X2 =e-2124. x'%3=1X; X1 = e3tX2 = e2t-1-21I-2-3х; X1 —25. x'3e2t-5te-St6.-72e2tX2 =Зе3e-5t-2226. x' =x; X1 = e' | 23-2 |0 11-22.3teSt-2 15. x'= y + z, y' = z + x, z' = x + y16. x' = 2x-3y, y' = x +y + 2z, z' = 5y – 7z17. x' = 3x – 4y +z +t, y' = x- 3z +t2, z' = 6y – 7z +t3%3D18. x' tx - y +e'z, y' = 2x +ty- z, z' = ex + 3ty +13zIn Pdica19. x = x2, x, = 2x3, x = 3x4, x = 4x1— 3х4, Хд31.20. x, = x2 + x3 + 1, x, = x3 + x4 + t,32.x3 =x1 + x4 + t², x, = x1 + x2 +t³433.34.In Problems 21 through 30, first verify that the given vectorsare solutions of the given system. Then use the Wronskian toshow that they are linearly independent. Finally, write theeral solution of the system.35.gen-36.メ=|42X; X1 =2e'e2t-e2t21. х'37.-3 -1–3e'X2 =27X; X1 =4-322. x'e3r2e-2t38.-3X2 =3e3te-2tతే శీ ఖ శే కశII

Answered: Image /qna-images/answer/071fa796-b5c9-4641-8f08-8c5fee0b8dc0.jpg

Answered: Wronskian

Math

Advanced Math

Wronskian

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

Need help for #23

al Equations
1
X; X1 = e2t
]**=
23. x'
5.
-3
4
X2 =
e-21
24. x'%3=
1
X; X1 = e3t
X2 = e2t
-1
-2
1
I
-2
-3
х; X1 —
25. x'
3e2t
-5t
e-St
6.
-7
2e2t
X2 =
Зе
3e-5t
-2
2
26. x' =
x; X1 = e' | 2
3
-2 |
0 1
1
-2
2.
3t
eSt
-2

15. x'= y + z, y' = z + x, z' = x + y
16. x' = 2x-3y, y' = x +y + 2z, z' = 5y – 7z
17. x' = 3x – 4y +z +t, y' = x- 3z +t2, z' = 6y – 7z +t3
%3D
18. x' tx - y +e'z, y' = 2x +ty- z, z' = ex + 3ty +
13z
In P
dica
19. x = x2, x, = 2x3, x = 3x4, x = 4x1
— 3х4, Хд
31.
20. x, = x2 + x3 + 1, x, = x3 + x4 + t,
32.
x3 =x1 + x4 + t², x, = x1 + x2 +t³
4
33.
34.
In Problems 21 through 30, first verify that the given vectors
are solutions of the given system. Then use the Wronskian to
show that they are linearly independent. Finally, write the
eral solution of the system.
35.
gen-
36.
メ=|
4
2
X; X1 =
2e'
e2t
-e2t
21. х'
37.
-3 -1
–3e'
X2 =
27
X; X1 =
4
-3
22. x'
e3r
2e-2t
38.
-3
X2 =
3e3t
e-2t
తే శీ ఖ శే కశ
II

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