Pdes

[gino492]

Having problems starting this question, I am not sure what formula to use and how to solve it. It says it's a heat equation but it looks more like a 1 dimensional wave equation. If I could get started I would be able to finish it, I literally just don't know how to start. Do I use burgers equation? Then use taylor? A few lines would be a great help.

Thanks

Gino

 

[HallsofIvy]

I am puzzled as to why you would think that was a wave equation. The wave equation is a "hyperbolic" equation: we have second derivatives with respect to both variables, on opposite sides of the equations: \(\displaystyle \frac{\partial^2f}{\partial x^2}= \frac{\partial^2 f}{\partial t^2}\). The heat equation is "parabolic"- there is a second derivative with respect to only one variable: \(\displaystyle \frac{\partial^2 f}{\partial x^2}= \frac{\partial f}{\partial t}\). This is clearly of the second kind.