Travelling waves 8² Which of the following are valid solutions of 2 ou 0x² □ (x − vt)² + (x+vt)² +1 □ (x − vt)² − (x + vt)² + 1 with initial condition du(x,0) dt # 0? 1 1 + (x+vt)²+1 (x-vt)²+1 0 (x+vt)² +1 (x-vt)² +1

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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Travelling waves
Which of the following are valid solutions of
d²u
dx²
1.0²u
c² Ət²
□ (x − vt)² + (x+vt)² +1
□ (x − vt)² – (x+vt)² + 1
du(x,0)
with initial condition
0?
Ət
□
1
1
(z+vt) ² +1 + (z-xt) ² +1
c-vt
1
1
(x+ut) ²+1 (z-vt) ² +1
(x+vt)²+1
Transcribed Image Text:Travelling waves Which of the following are valid solutions of d²u dx² 1.0²u c² Ət² □ (x − vt)² + (x+vt)² +1 □ (x − vt)² – (x+vt)² + 1 du(x,0) with initial condition 0? Ət □ 1 1 (z+vt) ² +1 + (z-xt) ² +1 c-vt 1 1 (x+ut) ²+1 (z-vt) ² +1 (x+vt)²+1
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