(a) Consider the differential equation y/ + p(t)y = g(t) with p(t) # 0. Show that this equation is not exact. (b) Let µ(t) = ef p(t)dt_ Show that the equation H(t)(y' + p(t)y) = H(t)g(t) is exact and solve it.
(a) Consider the differential equation y/ + p(t)y = g(t) with p(t) # 0. Show that this equation is not exact. (b) Let µ(t) = ef p(t)dt_ Show that the equation H(t)(y' + p(t)y) = H(t)g(t) is exact and solve it.
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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Question
![(a) Consider the differential equation
y + p(t)y = g(t)
with p(t) # 0. Show that this equation is not exact.
(b) Let µ(t) = eS P(?)dt_ Show that the equation
µ(t)(y/ + p(t)y) = µ(t)g(t)
is exact and solve it.
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd418c71c-f297-4f33-b9c0-48064ff82d75%2F7b5556c5-5ce7-4f6e-976c-d8ad28c8c4a7%2F8ort9ir_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Consider the differential equation
y + p(t)y = g(t)
with p(t) # 0. Show that this equation is not exact.
(b) Let µ(t) = eS P(?)dt_ Show that the equation
µ(t)(y/ + p(t)y) = µ(t)g(t)
is exact and solve it.
2
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