Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = ³ and 2 = ex. Think of the corresponding vector solutions ₁ and 2 and use the Wronskian to show that the solutions are linearly independent. Wronskian = det | These solutions are linearly independent because the Wronskian is Choose for all x.
Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = ³ and 2 = ex. Think of the corresponding vector solutions ₁ and 2 and use the Wronskian to show that the solutions are linearly independent. Wronskian = det | These solutions are linearly independent because the Wronskian is Choose for all x.
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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please solve both 2 parts
Transcribed Image Text:,3x
Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = ³x
and ze
ex. Think of the corresponding vector solutions ₁ and 2 and use the Wronskian to show that the
solutions are linearly independent.
Wronskian = det
TE
These solutions are linearly independent because the Wronskian is
Choose
✓for all x.
![Use the Wronskian to determine whether the functions y₁
=
Wronskian = det
[
sin(2x) and y2 = cos(6x) are linearly independent.
]
=
These functions are linearly independent because the Wronskian is nonzero for Choose value(s) of x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05295cc1-71f0-4e3b-b6f8-2c1731c6d617%2F9dc4d7e0-ac86-444a-8786-6da9a21135f8%2Fg6m3xl_processed.png&w=3840&q=75)
Transcribed Image Text:Use the Wronskian to determine whether the functions y₁
=
Wronskian = det
[
sin(2x) and y2 = cos(6x) are linearly independent.
]
=
These functions are linearly independent because the Wronskian is nonzero for Choose value(s) of x.
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