''..Cauchy stress tensor in every material point in the body satisfy the equilibrium equations.''
\sigma_{ij,j}+F_i=0
I would appreciate if you could write out what it means.
Also there is this notation which I don't understand:
\frac{\partial}{\partial y_j}\sigma_{ij}(x,y)
u''tt=a^2*u''xx + t*x 0<x<l; t>0
u(0,t)=u(l,t)=0
u(x,0)=u't(x,0)=0
http://eqworld.ipmnet.ru/en/solutions/lpde/lpde202.pdf
^^Here i found how to solve this problem using Green's function, however i am told to solve this using the method of separation of variables. But i cannot find any theory...