Question: Is this a standard PDE ?

Can one find an integral representation of the solution of the following system of PDEs?

pde1 := diff(f(x,y),x) + A(x) * ( p11* f(x,y) + p12 + p13*x ) 
= p14 * B(y)/B(x) * diff(f(x,y),x);

pde2 := diff(f(x,y),y) + A(y) * ( p21* f(x,y) + p22 + p23*y ) 
= p24 * B(x)/B(y) * diff(f(x,y),y);

f(x,y) is the unknown function,
A(x) and B(x) are known functions,
p11, p12, etc. are real parameters.

If p14=0 and p24=0, the right-hand side is equal to zero and the system reduces to a linear system of two independent ODEs.

But I'm interested in the case where at least one of  p14 or p24 is non-zero.

Is this a standard PDE system? I'm not familiar with PDEs (I am reasonably familiar with the basics of ODEs, but don't know anything at all about PDEs).

The following special case would already be something (it looks quite a bit easier, but looks aren't everything),

eval({pde1,pde2},{p11=0,p21=0});

or maybe this one:

eval({pde1,pde2},{p11=0,p21=0,p24=0});

Thanks!