Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (xo, Yo) in the region. (25 - y²)y' = x² O A unique solution exists in the region consisting of all points in the xy-plane except (0, 5) and (0, -5). O A unique solution exists in the regions y < -5, -5 < y < 5, and y> 5. O A unique solution exists in the region y < 5. O A unique solution exists in the region y> -5. O A unique solution exists in the entire xy-plane.
Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (xo, Yo) in the region. (25 - y²)y' = x² O A unique solution exists in the region consisting of all points in the xy-plane except (0, 5) and (0, -5). O A unique solution exists in the regions y < -5, -5 < y < 5, and y> 5. O A unique solution exists in the region y < 5. O A unique solution exists in the region y> -5. O A unique solution exists in the entire xy-plane.
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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Transcribed Image Text:Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (xo, Yo) in the region.
(25 - y²)y' = x²
O A unique solution exists in the region consisting of all points in the xy-plane except (0, 5) and (0, -5).
O A unique solution exists in the regions y < -5, -5 < y < 5, and y> 5.
O A unique solution exists in the region y < 5.
O A unique solution exists in the region y > -5.
O A unique solution exists in the entire xy-plane.
Transcribed Image Text:Find an explicit solution of the given initial-value problem.
1
y(6) = 6
y =
dy
dx
=
y²
x²
1
1
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