4. Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that dv/dt = -kv. a. Show that its velocity and position at time t are given by and v(t)= voe -kt x(t) = x + (%) (1 − e¯kt). b. Conclude that the body travels only a finite distance, and find that distance.
4. Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that dv/dt = -kv. a. Show that its velocity and position at time t are given by and v(t)= voe -kt x(t) = x + (%) (1 − e¯kt). b. Conclude that the body travels only a finite distance, and find that distance.
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:c. r² tan(y)y' + tan(y)y'
4. Suppose that a body moves through a resisting medium with resistance proportional
to its velocity v, so that dv/dt = -kv.
a. Show that its velocity and position at time t are given by
v(t) = voe
and
=
-kt
x(t) = x + ( ) (1 − e¯kt).
VO
k
b. Conclude that the body travels only a finite distance, and find that distance.
5. Determine whether or not the initial value problem
dy
dx
has a solution. Is the solution unique?
6. Determine whether or not the initial value problem
dy
Vy; y(0) = 0
dx
has a solution. Is the solution unique?
√xy; y(2) = 1
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