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a) What conditions on the functions g(t) and h(t) must be satisfied for the differential equation to be exact? dx g(t). +h(t)x = 0 dt

a) What conditions on the functions g(t) and h(t) must be satisfied for the differential equation to be exact? dx g(t). +h(t)x = 0 dt

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) What conditions on the functions g(t) and h(t) must be satisfied for the differential equation to be exact? dx dt g(t)- +h(t)x = 0
Transcribed Image Text:a) What conditions on the functions g(t) and h(t) must be satisfied for the differential equation to be exact? dx dt g(t)- +h(t)x = 0
b) What is the solution of the differential equation in a) when these conditions are satisfied? c) Solve the initial value problem (1 + cos² t) dx dt x sin 2t = 2t² + 4t +4, x(0) = 2
Transcribed Image Text:b) What is the solution of the differential equation in a) when these conditions are satisfied? c) Solve the initial value problem (1 + cos² t) dx dt x sin 2t = 2t² + 4t +4, x(0) = 2
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