'% Exercise 1: [5 Marks] Suppose a(z) is continuous on the half-open interval 0 < x≤ 1. What additional condition must a(z) satisfy so that every solution of the scalar differential equation: dy = a(z)y, for 0 < x≤1 has the property a) y(z) 0, as → +0? →0, as Investigated Lb) y(z) I → + +0? as xo all) the same question for the differential equation: dy dz where only solutions with 0 < y(x) ≤ 1/e are taken into consideration. = a(z)y ln(²), for 0 < x ≤ 1
'% Exercise 1: [5 Marks] Suppose a(z) is continuous on the half-open interval 0 < x≤ 1. What additional condition must a(z) satisfy so that every solution of the scalar differential equation: dy = a(z)y, for 0 < x≤1 has the property a) y(z) 0, as → +0? →0, as Investigated Lb) y(z) I → + +0? as xo all) the same question for the differential equation: dy dz where only solutions with 0 < y(x) ≤ 1/e are taken into consideration. = a(z)y ln(²), for 0 < x ≤ 1
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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Exercise 1: [5 Marks] Suppose a(z) is continuous on the half-open
interval 0 < x≤ 1. What additional condition must a(z) satisfy so that
every solution of the scalar differential equation:
dy = a(z)y, for 0 < x≤1
has the property
a) y(z) 0, as → +0?
→0, as
Investigated
Lb) y(z)
I
→
+
+0?
as xo
all)
the same question for the differential equation:
dy
dz
where only solutions with 0 < y(x) ≤ 1/e are taken into consideration.
= a(z)y ln(²), for 0 < x ≤ 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53564e68-6556-4f4f-99fb-86f326064fe5%2Fd3c58848-5f16-41e6-95c4-f7e73607c703%2Fgryzo5h_processed.png&w=3840&q=75)
Transcribed Image Text:'%
Exercise 1: [5 Marks] Suppose a(z) is continuous on the half-open
interval 0 < x≤ 1. What additional condition must a(z) satisfy so that
every solution of the scalar differential equation:
dy = a(z)y, for 0 < x≤1
has the property
a) y(z) 0, as → +0?
→0, as
Investigated
Lb) y(z)
I
→
+
+0?
as xo
all)
the same question for the differential equation:
dy
dz
where only solutions with 0 < y(x) ≤ 1/e are taken into consideration.
= a(z)y ln(²), for 0 < x ≤ 1
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