python - PDE solver that handles constraints -

i trying solve system of partial differential equations of general form

f(f(x,y), f'(x,y), f''(x,y), g(x,y), g'(x,y), g''(x,y)) = 0 

where derivatives may taken respect both x , y , f(x,y) , g(x,y) subject constraint

g(f(x,y),g(x,y)) = 0 

i wonder if there exists (preferably python based) solver (not method, know methods) can deal problem of kind? appreciate , apologise if question seems general.

such problem require initial conditions , boundary conditions satisfied obtain unique solution. need provide domain (geometry) solver. think must @ finite element solvers in python.

just quick google search provided few finite element solvers in python, have not tested any. guess starting point.