4. (Separation) Seeking a solution u(x, t) = X(x)T(t) for the given PDE, carry out steps analogous to equations (3)?(6), and derive ODE's analogous to (7a,b). Take the separation constant to be ?K2, as we do in (6). Obtain general solutions of those ODE's (distinguishing any special ic values, as necessary) and use superposition to obtain a solution analogous to the solution (13) of (1 a). if the PDE cannot be separated, state that.
(b) uxx + 2ux = Ut HINT: In this case you should find that the value of K that needs to be distinguished Las we distinguished the case K. = 0 in (9) and (10)1 is N. = 1, not K = 0.
(Please view the attachment starting with hw5-1, hw5-1', and hw5-1''.)
Hello and thank you for posting your question to Brainmass!
The solution is attached below (next to the paperclip icon) in two formats. one is in Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.
The equation is separable.
We start by defining:
Since X(x) is a function of x ...
Separation of vairbles and diffusion equations are investigated. The solution is detailed and well presented.