Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Question:**
On what region of the xy-plane does the differential equation have a unique solution that satisfies the given initial condition?
\[
(9 - y^2)y' = x^2, \quad y(-3) = -4
\]
**Options:**
a. A unique solution exists in the regions \( y < -3 \).
b. A unique solution exists in the region \( y \neq \pm 3 \).
c. A unique solution exists in the region consisting of all points in the xy-plane except \((0,3)\) and \((0,-3)\).
d. A unique solution exists in the region \(-3 < y < 3\).
e. A unique solution exists in the entire xy-plane.](https://content.bartleby.com/qna-images/question/1300845a-828a-484d-8f06-319293900125/1ba386ec-a12c-47f6-a8f2-d28533479282/6jucte_processed.png)
Transcribed Image Text:**Question:**
On what region of the xy-plane does the differential equation have a unique solution that satisfies the given initial condition?
\[
(9 - y^2)y' = x^2, \quad y(-3) = -4
\]
**Options:**
a. A unique solution exists in the regions \( y < -3 \).
b. A unique solution exists in the region \( y \neq \pm 3 \).
c. A unique solution exists in the region consisting of all points in the xy-plane except \((0,3)\) and \((0,-3)\).
d. A unique solution exists in the region \(-3 < y < 3\).
e. A unique solution exists in the entire xy-plane.
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