How to use Matlab to solve this PDE?

I have a PDE problem to solve. Could anyone solve this problem with the tool in matlab? Please don't use the finite difference method. The problem is as followed:

Governing equation:

Utt=sin(a*t)*Uxx;

Boundary Conditions: U(0,t)=0; U(L,t)=0;

Initial Conditions: Ut(x,0)=0; U(x,0)=sin(6*pi*x/L);

where 'a'is a constant, you can give a positive value to it.

'U' is a form about x and t;

'Utt' means U double prime of t; 'Uxx' means U double prime of x;

'Ut'means U prime of t.