Self adjoint differential equation?

[vivek.iitd]

Hello everyone, could you please make me understand, what are self-adjoint equations? and how can we convert a differential equation into a self-adjoint form?

Thank you.

 

[hunt_mat]

Let $T$ by the differential equation and denote an inner product by:
$$(v,Tu)=\int vTudx$$
If
$$(T^{\star}v,u)=(v,Tu)$$
Then the differential operator is self adjoint.