Let g(s,t) = As'" - cost, cost – s"), which of the following is true?O A. -sint E+ 11s10= 0atcostOsog= 0costOB 11s1011s10agsints10 costog= 0O D. No correct answersint11s10Osôgcost= 0at

Name: Let g(s,t) = As'" - cost, cost – s"), which of the following is true?
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Description: Let g(s,t) = As'" - cost, cost – s"), which of the following is true?O A. -sint E+ 11s10= 0atcostOsog= 0costOB 11s1011s10agsints10 costog= 0O D. No correct answersint11s10Osôgcost= 0at

Answered: Let g(s,t) = As" - cost, cost -s"),…

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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Let g(s,t) = As'" - cost, cost – s"), which of the following is true?
O A. -sint E
+ 11s10
= 0
at
cost
Os
og
= 0
cost
OB 11s10
11s10
ag
sint
s10 cost
og
= 0
O D. No correct answer
sint
11s10
Os
ôg
cost
= 0
at

Expert Solution

Step 1

$g i v e n g (s, t) = f (s^{11} - \cos t, \cos t - s^{11}) x = s^{11} - \cos t, y = \cos t - s^{11} d i f f e r e n t i a t e p a r t i a l l y g w . r . t o s a n d t \frac{\partial g}{\partial s} = \frac{\partial g}{\partial x} \frac{\partial x}{\partial s} + \frac{\partial g}{\partial y} \frac{\partial y}{\partial s} \frac{\partial g}{\partial s} = 11 s^{10} \frac{\partial g}{\partial x} - 11 s^{10} \frac{\partial g}{\partial y} = 11 s^{10} (\frac{\partial g}{\partial x} - \frac{\partial g}{\partial y}) \dots (i) \frac{\partial g}{\partial t} = \frac{\partial g}{\partial x} \frac{\partial x}{\partial t} + \frac{\partial g}{\partial y} \frac{\partial y}{\partial t} \frac{\partial g}{\partial t} = \sin t \frac{\partial g}{\partial x} - \sin t \frac{\partial g}{\partial y} = \sin t (\frac{\partial g}{\partial x} - \frac{\partial g}{\partial y}) \dots (i i) d i v i d e (i) b y (i i) \frac{\frac{\partial g}{\partial s}}{\frac{\partial g}{\partial t}} = \frac{11 s^{10} (\frac{\partial g}{\partial x} - \frac{\partial g}{\partial y})}{\sin t (\frac{\partial g}{\partial x} - \frac{\partial g}{\partial y})} = \frac{11 s^{10}}{\sin t} \sin t \frac{\partial g}{\partial s} = 11 s^{10} \frac{\partial g}{\partial t} \sin t \frac{\partial g}{\partial s} - 11 s^{10} \frac{\partial g}{\partial t} = 0 - \sin t \frac{\partial g}{\partial s} + 11 s^{10} \frac{\partial g}{\partial t} = 0$

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