Inhomogeneous wave equation help

In summary, the conversation is about solving a differential equation with the given conditions. The speaker shares their progress in finding the homogeneous part and asks for help with the next steps. Another speaker suggests a trial solution and the first speaker follows their advice. Eventually, the first speaker finds the final solution and expresses gratitude for the help received.
  • #1
finmath
2
0
I need help solving 3Utt+10Uxt+3Uxx=sin(x+t)

I have found the homogeneous part, which is U(x,t)=f(3x-t) +g(x-3t), but I don't know where to go from there. Any help would be much appreciated!
 
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  • #2
Well, make a trial solution [tex]U_{p}(x,t)=A\sin(x+t)[/tex] and see if you can determine what "A" must be. :smile:
 
  • #3
Back to the basics! For some reason I thought it was going to be way more difficult.
My final solution is U(x,t)=f(3x-t) + g(x-3t) - sin(x+t)/16

Thanks for your help! :smile:
 
  • #4
arildno said:
Well, make a trial solution [tex]U_{p}(x,t)=A\sin(x+t)[/tex] and see if you can determine what "A" must be. :smile:

I though the try function should be of the form

[tex]U_{p}(x,t)=A\sin(x+t) + B\cos(x+t)[/tex]
 
  • #5
And B will be 0..:smile:
 

1. What is an inhomogeneous wave equation?

An inhomogeneous wave equation is a type of partial differential equation that describes the propagation of a wave in a medium that is not uniform. This means that the properties of the medium, such as density and elasticity, vary throughout the space in which the wave is traveling.

2. How is an inhomogeneous wave equation different from a homogeneous wave equation?

A homogeneous wave equation describes the propagation of a wave in a medium that is uniform, meaning its properties do not change throughout the space. In contrast, an inhomogeneous wave equation takes into account the varying properties of the medium, making it a more complex equation to solve.

3. What are some real-life applications of inhomogeneous wave equations?

Inhomogeneous wave equations are used in many fields of science and engineering, such as acoustics, electromagnetics, fluid dynamics, and seismology. They are used to model and predict the behavior of waves in different types of media, such as air, water, and solids.

4. How do you solve an inhomogeneous wave equation?

Solving an inhomogeneous wave equation involves using mathematical techniques, such as separation of variables, Fourier transforms, and Green's functions. The specific method used depends on the specific form of the equation and the boundary conditions of the problem.

5. What are the limitations of inhomogeneous wave equations?

Inhomogeneous wave equations are limited in their ability to accurately describe the behavior of waves in highly complex and nonlinear media. They also do not take into account the effects of dispersion and dissipation, which can affect the propagation of waves in real-world situations.

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