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Fast help please: solving differential equations

  • #1

Homework Statement


I have the equation -(ck^2)U(k,t)=d^2/dt U(k,t). And I need to find the general solution.


Homework Equations





The Attempt at a Solution


I can rearrange this into the form d^2 U/dt^2 + (ck^2)U(k,t)=0 but I am not sure of the form of the solution to this equation.

could someone please give me pointer in the right direction
 

Answers and Replies

  • #2
Is it just U(k,t) = Acos(ckt)+Bcos(ckt)?
 
  • #3
Yeah, it's just the differential equation for SHM so that is the solution.
 
  • #4
dx
Homework Helper
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No it's not. You will get a constant when you do the integration with respect to t, and this constant can depend on k. So the general solution is what you wrote + f(k), where f(k) is an arbitrary function of k.

EDIT: You should have (√c)k instead of ck in the sin and cos.
 
  • #5
dx
Homework Helper
Gold Member
2,011
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Oops! I'm extremely sorry, my previous post is wrong. The constants A and B are the constants of integration, and they should be arbitrary functions of k.
 

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