On what region of the xy-plane does the differential equation would have a unique solution that satisfies the given initial condition. (y²1)y'=x, y(-3)=0 A uniquesolution exists in the regions y< - 1. A unique solution exists in the regiony y* + 1. A unique solution exists in the region consisting of all points in the xy-plane except (0, 1) and (0, -1). d. A unique solution exists in the regiony - 1
On what region of the xy-plane does the differential equation would have a unique solution that satisfies the given initial condition. (y²1)y'=x, y(-3)=0 A uniquesolution exists in the regions y< - 1. A unique solution exists in the regiony y* + 1. A unique solution exists in the region consisting of all points in the xy-plane except (0, 1) and (0, -1). d. A unique solution exists in the regiony - 1
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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![**Problem Statement:**
On what region of the xy-plane does the differential equation have a unique solution that satisfies the given initial condition?
**Differential Equation:**
\[
(y^2 - 1)y' = x, \quad y(-3) = 0
\]
**Options:**
a. A unique solution exists in the regions \( y < -1 \).
b. A unique solution exists in the region \( y \neq \pm 1 \).
c. A unique solution exists in the region consisting of all points in the xy-plane except \( (0,1) \) and \( (0,-1) \).
d. A unique solution exists in the region \( -1 < y < 1 \).
e. A unique solution exists in the entire xy-plane.
**Answer Choices:**
- ○ a
- ○ b
- ○ c
- ○ d
- ○ e](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1300845a-828a-484d-8f06-319293900125%2Ff08c07ee-dcb4-4432-897f-c10b03c78a93%2F5mvsjgm_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
On what region of the xy-plane does the differential equation have a unique solution that satisfies the given initial condition?
**Differential Equation:**
\[
(y^2 - 1)y' = x, \quad y(-3) = 0
\]
**Options:**
a. A unique solution exists in the regions \( y < -1 \).
b. A unique solution exists in the region \( y \neq \pm 1 \).
c. A unique solution exists in the region consisting of all points in the xy-plane except \( (0,1) \) and \( (0,-1) \).
d. A unique solution exists in the region \( -1 < y < 1 \).
e. A unique solution exists in the entire xy-plane.
**Answer Choices:**
- ○ a
- ○ b
- ○ c
- ○ d
- ○ e
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