Determine all the singular points of the given differential equation. (2-21-3)x"+(t+1)x'-(t-3)x=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA The singular points are all ts OB. The singular points are all ts and t = (Use a comma to separate answers as needed.) OC. The singular point(s) is/are t = (Use a comma to separate answers as needed.) OD. The singular points are all tz and t= (Use a comma to separate answers as needed.) OE. The singular points are all t OF. There are no singular points.
Determine all the singular points of the given differential equation. (2-21-3)x"+(t+1)x'-(t-3)x=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA The singular points are all ts OB. The singular points are all ts and t = (Use a comma to separate answers as needed.) OC. The singular point(s) is/are t = (Use a comma to separate answers as needed.) OD. The singular points are all tz and t= (Use a comma to separate answers as needed.) OE. The singular points are all t OF. There are no singular points.
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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3
![**Differential Equation Singular Points Analysis**
**Problem Statement:**
Determine all the singular points of the given differential equation:
\[
(t^2 - 2t - 3)x'' + (t + 1)x' - (t - 3)x = 0
\]
**Question:**
Select the correct choice from below and, if necessary, fill in the answer box to complete your choice.
**Choices:**
- **A.** The singular points are all \( t \leq\) [Blank]
- **B.** The singular points are all \( t \leq\) [Blank] and \( t =\) [Blank]
*(Use a comma to separate answers as needed.)*
- **C.** The singular point(s) is/are \( t =\) [Blank]
*(Use a comma to separate answers as needed.)*
- **D.** The singular points are all \( t \geq\) [Blank] and \( t =\) [Blank]
*(Use a comma to separate answers as needed.)*
- **E.** The singular points are all \( t \geq\) [Blank]
- **F.** There are no singular points.
**Explanation:**
To identify singular points, we check where the coefficients of the highest derivative or leading terms of the equation become zero or undefined. For the given equation, we focus on the coefficient of the second derivative (\(x''\)), which is \(t^2 - 2t - 3\). Finding the roots of this quadratic will help identify potential singular points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa827acfe-a0bc-46c0-ab61-62657df3b5db%2F44db9931-a045-4d62-9b67-1aa122d0269a%2Fnmshun5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Differential Equation Singular Points Analysis**
**Problem Statement:**
Determine all the singular points of the given differential equation:
\[
(t^2 - 2t - 3)x'' + (t + 1)x' - (t - 3)x = 0
\]
**Question:**
Select the correct choice from below and, if necessary, fill in the answer box to complete your choice.
**Choices:**
- **A.** The singular points are all \( t \leq\) [Blank]
- **B.** The singular points are all \( t \leq\) [Blank] and \( t =\) [Blank]
*(Use a comma to separate answers as needed.)*
- **C.** The singular point(s) is/are \( t =\) [Blank]
*(Use a comma to separate answers as needed.)*
- **D.** The singular points are all \( t \geq\) [Blank] and \( t =\) [Blank]
*(Use a comma to separate answers as needed.)*
- **E.** The singular points are all \( t \geq\) [Blank]
- **F.** There are no singular points.
**Explanation:**
To identify singular points, we check where the coefficients of the highest derivative or leading terms of the equation become zero or undefined. For the given equation, we focus on the coefficient of the second derivative (\(x''\)), which is \(t^2 - 2t - 3\). Finding the roots of this quadratic will help identify potential singular points.
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