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 general solution of the system. x′= 19−12 20−19x;x1=e11t 3 2,x2=e−11t 2 5 19−12 20−19x1= 19−12 20−19• 3e11t 2e11t=nothing=x1′ 19−12 20−19x2= 19−12 20−19• 2e−11t 5e−11t=nothing=x2′The Wronskian of the solutions isW=nothing.Are the solutions linearly independent? First verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearlyindependent Finally, write the general solution of the systen.19-12x, x, = e 11t- 19X'X2 =11t2019- 1219 - 123e 11t20 - 1920 - 192e11t19 - 1219 - 122e--11tX220 - 19- 19205e-11tThe Wronskian of the solutions is W =Are the solutions linearly independent?O YesO NoThe general solution is x(t) =%3D

i just substtuted the values X1 and X2 in system and verified that they are solutions and then by…

Answered: First verify that hie independent.…

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

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 general solution of the system.

x′=

	19	−12
20	−19

x1=e11t

	3
2

x2=e−11t

	2
5

	19	−12
20	−19

x1=

	19	−12
20	−19

•

	3e11t
2e11t

=nothing=x1′

	19	−12
20	−19

x2=

	19	−12
20	−19

•

	2e−11t
5e−11t

=nothing=x2′

The Wronskian of the solutions is

W=nothing.

Are the solutions linearly independent?

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 general solution of the systen.
19
-12
x, x, = e 11t
- 19
X'
X2 =
11t
20
19
- 12
19 - 12
3e 11t
20 - 19
20 - 19
2e11t
19 - 12
19 - 12
2e-
-11t
X2
20 - 19
- 19
20
5e-11t
The Wronskian of the solutions is W =
Are the solutions linearly independent?
O Yes
O No
The general solution is x(t) =
%3D

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