2.28c. Show that the equation may be simplified to
Solve this equation and write the solution in terms of and .
2.28b. Reduce to canonical form II. In 2.23 you diagonalized
essentially the same equation by rotating the coordinate system; and
you could then have stretched the coordinates to reduce it to the
Laplace equation. Are the coordinates that you find now equivalent
to those? In particular, are the lines of constant and
orthogonal like in 2.23? If not, how come that more than one linear
coordinate transformation can turn the equation into the Laplace
equation?
3.41. This is similar to the Laplace version discussed earlier
in class. Describe the reason that there is no solution physically,
considering it as a heat conduction problem in a circular plate.