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On what region of the xy-plane does the differential equation would have a unique solution that satisfies the given initial condition. (9-y²)y'=x², y(-3)=-4 a. A uniquesolution exists in the regions y < -3. b. A unique solution exists in the regiony y * ± 3. C. A unique solution exists in the region consisting of all points in the xy-plane except (0,3) and (0, -3). A unique solution exists in the regiony -3

On what region of the xy-plane does the differential equation would have a unique solution that satisfies the given initial condition. (9-y²)y'=x², y(-3)=-4 a. A uniquesolution exists in the regions y < -3. b. A unique solution exists in the regiony y * ± 3. C. A unique solution exists in the region consisting of all points in the xy-plane except (0,3) and (0, -3). A unique solution exists in the regiony -3

Advanced Engineering Mathematics
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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**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.
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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