Write the solution of the following Cauchy problem for the wave equa-3.tion as a sum of a forward wave and a backward wave and sketch its graph att = 0, 1, 2 & 3:Uu = U -0 0,S4 - a2, -2 < S 2u(x, 0) = 6(x) =elsewhereu(x, 0) = 0,-00

Given that, utt=uxx, -∞<x<∞, t>0,ux,0=ϕx=4-x2, -2≤x≤20, elsewhereutx,0=0=gx,…

Answered: 3. tion as a sum of a forward wave and…

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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13. [P] Particle 1 starts at point (3, 1, 1) and particle 2 starts at point (10,5,-4); at t = 0, both particles begin to move along linear paths. After 1 second, particle 1 is at point (4, 3, 4) and particle 2 is at (8, 6, 3). (a) Do the paths of the particles intersect? (b) Will the particles collide?
11:PP A docs.google.com/forms/d/e O = The real part for the function f(z) = 4z2 – 2z + 9 إجابتك = The imaginary part for the function f(z) = 4z² – 2z + 9 إجابتك = Ux f(z) = 4z² – 2z + 9 إجابتك Uy
21. (a) Use Newton's method to find the root of the equation r – xª + 3x2 – 3x – 2 = 0 in the interval [1,2] correct to six decimal places. (b) Use Newton's method to find the root of the equation 3x4 – 8x3 +2 = 0 in the interval [2,3] correct to six decimal places. 22. A particle is moving with the given data. Find the position of the particle. (a) v (t) = 3t – R, s (0) = 1. (b) a (t) = 2 sint + 3 cos t, s (0) = 0, v (0) = 2. 1+t² >
6) f(x, y) = 2x +3.xy +4y-5x+2y Ans. f(2,-1) = -6 local min.
Determine the solutions of the following first-order ODEs: Tip:y'=xv'+v y=xv * xv'+v=(4xv-3x)/(2x-xv) >>>> xv'+v=(2v-3)/(1-v)>>>xv'=(2v-3-v+v²)/(1-v) * >>>>>>>>>** ANSWER CORRECT :|y − x| = C|y + x|3 **<<<<<< *****The answer |y − x| = C|y + 3x|5 is considered wrong ( will not be accepted as it will be considered wrong)*****
8x'z +62yz +9y'z factors to O <{8x² +6xy = 9y²) O (8x° +6.xy +9y*) to search F7 F8 F9 F10 F3 F4 F5 F6 F2 $ % 2 3 4 5 6 8
(6) Determine F'(-3i) if 522 – 4z + 3 a) = / " - dz, F(« C where C is the ellipse 16x² + 9y² = 144.
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3. tion as a sum of a forward wave and a backward wave and sketch its graph at t= 0,1,2 & 3: Write the solution of the following Cauchy problem for the wave equa- U -00 0, u(z,0) = 6(x) = {4- z, -25152 (0. elsewhere u(z,0) = 0, -00