Is this pde analytically solvable?

[nigels]

I'm a theoretical biologist in the process of developing a spatial model for animal movement. So far, I've arrived at the following structure of an equation (see attachment):
*theta is just some function of x and t.

Having never formally studied pde, I'm wondering whether one can, from this, derive an analytical solution to y(x,t) and, if so, how (or, what sources can I go to to find the solution)?

 

[Matterwave]

I don't see an attachment...

 

[nigels]

hope it works this time

https://www.physicsforums.com/attachment.php?attachmentid=34793&d=1303613043

 

[JJacquelin]

I'm wondering whether one can, from this, derive an analytical solution to y(x,t)

Analytical solution can or cannot be derived, depending the form of the function theta(x,t)
What is the function theta(x,t) ?