# drumhead problem
# u_{tt} = c^2(laplacian u), u=0 on clamped edge
# position and velocity given
# Separation of variables leads to the following DE to be solved:
lambda:='lambda':de:=diff(R(r),r,r)*r+diff(R(r),r)+lambda^2*r*R(r)=0;
dsolve(de,R(r));
with(DEtools):
lambda:=2:odeadvisor(de); # Advice on what kind of equation is being solved
# ?odeadvisor,types
# ?dsolve
# ?Bessel
# Plots of Bessel functions of first and second kind
plot(BesselJ(0,2*r),r=0..40);
BesselK(0,0);plot(BesselY(0,2*r),r=0..40);