(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
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(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
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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