Consider the wave equation
when the solution s admits spherical symmetry, ie, s(t,x,y,z)=v(t,r), where ... , the wave equation becomes:
making the substitution
for some twice differentiable function h, show that (1) becomes
hence, show that the general solution reads
for any twice differentiable functions f and g.
look at partial v(r,t) with r yields -1/r^2 [f(r-ct) +g(r+ct)] +1/r[fr(r-ct) +gr(r+ct)]
Then multiply this by r^2 to get:
-1[f(r-ct) +g(r+ct)] +r[fr(r-ct) ...
A wave equation is investigated.