1. Let p(x), a(x) and B(x) be three functions of r. Consider the PDE of u(r, t): PEx) at (a) (10 ...
1. Let p(x), a(x) and B(x) be three functions of r. Consider the PDE of u(r, t): PEx) at (a) (10 pt) Show that the method of separation of variables works only if ρ(r) equals to a constant. (b) (10 pt) Assumefor some constant c. Show that the spatial equation (the differential equation about the spatial variable r) is of Sturm-Liouville type. B(z)
1. Let p(x), a(x) and B(x) be three functions of r. Consider the PDE of u(r, t): PEx) at (a) (10 pt) Show that the method of separation of variables works only if ρ(r) equals to a constant. (b) (10 pt) Assumefor some constant c. Show that the spatial equation (the differential equation about the spatial variable r) is of Sturm-Liouville type. B(z)