The length L of a line on a sphere of radius r between two points, specified in the spherical coordinate system as (r, 0a, Þa) and (r, Ob, Pb), is given by the integral L = r Sb /[o'($)]² + sin? Odø. What ordinary differential equation does the function 0(4) Фа that describes the shortest such line satisfy? Select one: O 1. sin² e = 0. Vcos?+sin² o O 2. /(@)² + sin? 0 + = 0. O 3. sin² 0 C, where C is some constant. V(os2+sin²o О 4. = 0. O 5. /(@)² + sin? 0 + C, where C is some constant. O6. V(@)2 + sin? 0 = C, where C is some constant.
The length L of a line on a sphere of radius r between two points, specified in the spherical coordinate system as (r, 0a, Þa) and (r, Ob, Pb), is given by the integral L = r Sb /[o'($)]² + sin? Odø. What ordinary differential equation does the function 0(4) Фа that describes the shortest such line satisfy? Select one: O 1. sin² e = 0. Vcos?+sin² o O 2. /(@)² + sin? 0 + = 0. O 3. sin² 0 C, where C is some constant. V(os2+sin²o О 4. = 0. O 5. /(@)² + sin? 0 + C, where C is some constant. O6. V(@)2 + sin? 0 = C, where C is some constant.
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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![The length L of a line on a sphere of radius r between two points, specified in the spherical coordinate system as (r, 0a, Pa) and
(r, Ob, Pb), is given by the integral L = r
rob V [O ($)]² + sin? Odø. What ordinary differential equation does the function 0(4)
Фа
that describes the shortest such line satisfy?
Select one:
sin?e
0.
O 2. /(@)² + sin² 0 +
= 0.
О з.
sin²e
C, where C is some constant.
О4.
0.
O5.
+ sin? 0 +
C. where C is some constant.
O 6.
V(@')2 + sin? 0 = C, where C is some constant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53fddec7-3ea9-4573-acf2-c56db43d1c61%2F3c3d5090-6b89-4c7c-aa08-8c1bede44e6b%2F4n9n0u_processed.png&w=3840&q=75)
Transcribed Image Text:The length L of a line on a sphere of radius r between two points, specified in the spherical coordinate system as (r, 0a, Pa) and
(r, Ob, Pb), is given by the integral L = r
rob V [O ($)]² + sin? Odø. What ordinary differential equation does the function 0(4)
Фа
that describes the shortest such line satisfy?
Select one:
sin?e
0.
O 2. /(@)² + sin² 0 +
= 0.
О з.
sin²e
C, where C is some constant.
О4.
0.
O5.
+ sin? 0 +
C. where C is some constant.
O 6.
V(@')2 + sin? 0 = C, where C is some constant.
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