11. Suppose we know that the function f(t, y) is continuous and that f(1, 3) = -1 for all t. (a) What does this information tell us about the slope field for the differential equa- tion dy/dt = f(t, y)? (b) What can we conclude about solutions y(t) of dy/dt = f(t, y)? For example, if y(0) <3, can y(t) →∞ as t increases?
11. Suppose we know that the function f(t, y) is continuous and that f(1, 3) = -1 for all t. (a) What does this information tell us about the slope field for the differential equa- tion dy/dt = f(t, y)? (b) What can we conclude about solutions y(t) of dy/dt = f(t, y)? For example, if y(0) <3, can y(t) →∞ as t increases?
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:11. Suppose we know that the function f(t, y) is continuous and that f(1, 3) = -1 for
all t.
(a) What does this information tell us about the slope field for the differential equa-
tion dy/dt = f(t, y)?
(b) What can we conclude about solutions y(t) of dy/dt = f(t, y)? For example,
if y(0) <3, can y(t) →∞ as t increases?
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