Determine a region of the xy-plane for which the DE (1+ y) y' = x²will have a unique solution whose graph passes trough a point (xo, yo) in the region.
Determine a region of the xy-plane for which the DE (1+ y) y' = x²will have a unique solution whose graph passes trough a point (xo, yo) in the region.
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 DE
(1+ y ) y' = x²will have a unique solution whose graph
passes trough a point (xo, yo) in the region.
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Step 1
Theorem of existence of uniqueness: If and are continuous on rectangular region R, then there exists interval I on which unique exists.
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