Consider the family of functions uc(x,t) of two variables x,t, indexed by the parameter c, uc(x,y)=ln(x+ct)(cos(ct)cos(x)−sen(ct)sin(x)). Determine the value of the parameter c>0 so that the function uc(x,y) is a solution of the wave equation 13.∂^(2)uc/∂x^(2)−8.∂^(2)uc/∂t^(2)=0.

Consider the family of functions uc(x,t) of two variables x,t, indexed by the parameter c, uc(x,y)=ln(x+ct)(cos(ct)cos(x)−sen(ct)sin(x)). Determine the value of the parameter c>0 so that the function uc(x,y) is a solution of the wave equation 13.∂^(2)uc/∂x^(2)−8.∂^(2)uc/∂t^(2)=0.

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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Question

Consider the family of functions uc(x,t) of two variables x,t, indexed by the parameter c,
uc(x,y)=ln(x+ct)(cos(ct)cos(x)−sen(ct)sin(x)).
Determine the value of the parameter c>0 so that the function uc(x,y) is a solution of the wave equation

13.∂^(2)uc/∂x^(2)−8.∂^(2)uc/∂t^(2)=0.

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