Consider the first-order differential equation y'=f(x,y) and a point (a,b) in the plane. Which of the following statements is always true? O Iff is continuous on a rectangular region centered at (a,b), then f has a unique solution on that rectangular region. If f is continuous on a rectangular region centered at (a,b), then f has a solution on that rectangular region. If either for partial derivative off with respect to y is not continuous on a rectangular region centered at (a,b), then f has no unique solution on the rectangular region. If f or partial derivative off with respect to y are both continuous on a rectangular region centered at (a,b), then f has a unique solution on the plane.
Consider the first-order differential equation y'=f(x,y) and a point (a,b) in the plane. Which of the following statements is always true? O Iff is continuous on a rectangular region centered at (a,b), then f has a unique solution on that rectangular region. If f is continuous on a rectangular region centered at (a,b), then f has a solution on that rectangular region. If either for partial derivative off with respect to y is not continuous on a rectangular region centered at (a,b), then f has no unique solution on the rectangular region. If f or partial derivative off with respect to y are both continuous on a rectangular region centered at (a,b), then f has a unique solution on the 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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Consider the first-o
Transcribed Image Text:Consider the first-order differential equation y'=f(x,y) and a point (a,b) in the plane. Which of the following statements is always true?
O Iff is continuous on a rectangular region centered at (a,b), then f has a unique solution on that rectangular region.
If f is continuous on a rectangular region centered at (a,b), then f has a solution on that rectangular region.
If either for partial derivative off with respect to y is not continuous on a rectangular region centered at (a,b), then f has no unique solution on the rectangular region.
If f or partial derivative off with respect to y are both continuous on a rectangular region centered at (a,b), then f has a unique solution on the plane.
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