Match the direction fields labeled A through D with the differential equation below.M11MAXATTTY1 ////1117Aс4BXXXXXSTTTTTTIND-/// 1. y' = 2 cos x + sin y2. y'= 1 cos x cos y3. y'= 3 cos x cos y4. y' = cos x sin y-

Answered: 1. y' = 2. y'= 1 cos x cos y 3. y' = 3…

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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*x*y" + xy + (x? - }\v=o x >0 1 - ,V1=X 2 sinx the following equations satisfied by v and y =V1V. Which of %3D Select one: а. (x sinx)v" + (2x 2 cosx)v' = 0 b. 1 (x 2 sinx)v" +(2x 1 2 cosx)v = 0 C. 1 (x 2 sinx)v" +(2x cosx)v' = 0 d. 3 1 (x Z sinx)v" + (2x¯I cosx- x 2 sinx + x ² sinx)v' = 0 2 sinx + x 2 sinx)v' = 0
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2. Find exact value of (a) sin-(-1) (b) cos-11 (c) tan-1 /3 (d) sin(sin¬' 0.8) (e) tan-'(tan ) (f) sin-(sin 2) (hint: 2 radians, not 2 degree)
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Find y' where y = 22 sin-1 (cos (9 x)) – tan¬1 (6 x) Answer: -198 sin(9 x) y' = 1-cos2 (9 x) 1+36 x2 198 6 V1-cos2 (9 æ) 1+36 x2 y' = 198 – 1+36 x2 198 sin(9 x) /1-cos² (9 x) 1+36 x2 -198 + 1+36 x2 ||

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1. y' = 2. y'= 1 cos x cos y 3. y' = 3 cos x cos y 4. y' = cos x sin y = 2 cos x + sin y