x²y" - 9xy' + 24y = 0; x*, x°, (0, ). %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Consider the differential equation**
\[ x^2 y'' - 9xy' + 24y = 0; \quad x^4, x^6, \ (0, \ \infty). \]
Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval.
The functions satisfy the differential equation and are linearly independent since
\[ W(x^4, x^6) = \boxed{\text{non-zero value}} \neq 0 \quad \text{for } 0 < x < \infty. \]
Form the general solution.
\[ y = \boxed{\text{general form of the solution}} \]
**Explanation of Graphs or Diagrams:**
This exercise involves verifying solutions to a differential equation and checking their linear independence by computing the Wronskian. There are no graphs or diagrams provided in this text.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F293eb728-f902-4770-89ad-1f12ac16fee3%2Fa1b84f62-b123-4cb8-9066-19d4563cedef%2Flgg95ms_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider the differential equation**
\[ x^2 y'' - 9xy' + 24y = 0; \quad x^4, x^6, \ (0, \ \infty). \]
Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval.
The functions satisfy the differential equation and are linearly independent since
\[ W(x^4, x^6) = \boxed{\text{non-zero value}} \neq 0 \quad \text{for } 0 < x < \infty. \]
Form the general solution.
\[ y = \boxed{\text{general form of the solution}} \]
**Explanation of Graphs or Diagrams:**
This exercise involves verifying solutions to a differential equation and checking their linear independence by computing the Wronskian. There are no graphs or diagrams provided in this text.
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