In each case explain solution method, find general and IVP solutions. 1. y'+2y=1+2 cos t; y(0) =1 (Hint: sum of 2 particular solutions; trig. source cos(@t) gives a -sin(...)). Extra: Explain why all solutions fall within the range a - a² + @ Cos ...) + a' + o° 2 +o -1/2< y<3/2, at large t (Hint: sandwich DE between 2 constant sources)
In each case explain solution method, find general and IVP solutions. 1. y'+2y=1+2 cos t; y(0) =1 (Hint: sum of 2 particular solutions; trig. source cos(@t) gives a -sin(...)). Extra: Explain why all solutions fall within the range a - a² + @ Cos ...) + a' + o° 2 +o -1/2< y<3/2, at large t (Hint: sandwich DE between 2 constant sources)
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:In each case explain solution method, find general and IVP solutions.
1. y'+2y=1+2 cos t; y(0) =1 (Hint: sum of 2 particular solutions; trig. source cos(@t) gives
a
-sin(...)). Extra: Explain why all solutions fall within the range
a
-
a² + @ Cos ...) +
a' + o°
2
+o
-1/2< y<3/2, at large t (Hint: sandwich DE between 2 constant sources)
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