Show that the functiona(z, t) = bi sin )cos() + b sin cos( 2)Tct2nctbị sinCOSL+ b2 sinLCOSLwhere c, L, b1, b2 are nonzero constants with L > 0 and c > 0, is a solution to theone-dimensional wave equationc2.

Answered: Image /qna-images/answer/1bc6667b-2b96-4472-a335-9a6b7b627444.jpg

Answered: Show that the function Tct 2Tx 2nct COS…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

SOLVE THE FOLLOWING H.O.D.E
part b please
Q2) Solve the wave equation u=u 00 " XX 11 subject to u(0,t) = u(2,t) =0, t>0 and u(x,0)=0, u )=0, u,(x,0): = sin (3лx), 0
Assignment 6 Problem 4 (Please answer it correctly): If r(t)=cos(3t)i+sin(3t)j+8tk
えゅ+ 3×は) + 2×り =0 Draw the phase - plane portrait with some ypteal tragedertes.
O Verify that the u = Cos 4 t sin 2x Solution of Wave Equation with suitable C Verify that the function u- e sin wx is a Solution of the Heat Equation with Suitable c tan ) O Verify that the fanc tion u = is a Solution of the Laplace Eguation.
Find dy dx 1) y = -1/323 ; tan 3 2 y = sec¹ 5x 3) y = cos ¹2x 4) y = cot ¹ & 2 5) = y = sin¹ (X=1) 6) y = xcos ¹2x - 11/2/2 √ √1-4x² + tan¹ \/ /
6 a"M %3D ulo,t)= M(2,*) = 2 Solue the wave equation, fot all 3 cases.
Which of the following is most suitable solution for wave equation = c2? %3D at2 ax2 .(a) y = (AeP* + Be-P*)(Ce pt + De ept) (b) y = (Acos px + Bsin px)(Ccos cpt + Dsin cpt) (c) y = (Ax + B)(Ct + D) (d) y = (Aepx + Be-px)(Cep*t + De-ep*r) O a O b O c O d
Page 1 > of 2 ZOOM + 2. Prove the orthogonality of the sine function. Specifically, prove that (0, ifn' + n (n'пу) dy = a sin () ппу а а a if n' = = n. Hint: Y ou need to use the following relationships: 1 sin A sin B = F [cos(A - B) — сos(A + B)] sin ax lim = a x→0
S(1,9) =2Inc* + y° )• 3y° tan"), then prove that B.(i) If дхду дудх
A string with motionless ends at x = 0 and x = 1 vibrates according to the wave equation Fu Ət² and the initial velocity J²u dr² 1. Use separation of variables (show details) to solve the equation provided that the initial profile of the string is u(x,0) = 4 sin(2x) Ju 5- Ət It=0 = 0.

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

Show that the function Tct 2Tx 2nct COS TX u(x, t) = bị sin COS L + b2 sin L where c, L, b1, b2 are nonzero constants with L > 0 and c > 0, is a solution to the one-dimensional wave equation = c².