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6. A function y(t) satisfies the equation: 1 y' = 2 cos t Find all initial values y(0) = a such that (a) lim,»00 y(t) > 0. (b) lim,»00 y(t) < 0. (c) lim,»00 y(t) does not exist.

6. A function y(t) satisfies the equation: 1 y' = 2 cos t Find all initial values y(0) = a such that (a) lim,»00 y(t) > 0. (b) lim,»00 y(t) < 0. (c) lim,»00 y(t) does not exist.

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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A functiony(t) satisfies the equation: y′−12y= 2cos(t). Find all initial values y(0)=a such that

(a) limt→∞y(t)>0

(b) limt→∞y(t)<0

(c) limt→∞y(t) does not exist

6. A function y(t) satisfies the equation: 1 y' = 2 cos t Find all initial values y(0) = a such that (a) lim,»00 y(t) > 0. (b) lim,00 y(t) < 0. (c) lim,»0 y(t) does not exist.
Transcribed Image Text:6. A function y(t) satisfies the equation: 1 y' = 2 cos t Find all initial values y(0) = a such that (a) lim,»00 y(t) > 0. (b) lim,00 y(t) < 0. (c) lim,»0 y(t) does not exist.
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We have to solve the differential equation by integrating factor.

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