what is the solution for y in this peculiar ODE ?
with initial conditions :
moreover
The condition...
(1)
... means that is a function of the only so that the DE is...
(2)
... where ...
(3)
The (2) is a linear first order DE and its general solution is...
(4)
The constant c is derived [when possible...] from the 'initial conditions' ...
Kind regards
thanks , that was really helpful . but i stated the simplest form the problem in hand , where A , B , and y are functions of the single variable x . but the real case requires that the latter functions could be functions of an arbitrary number of independent variables and the equation becomes :
where
is a unit volume (so to speak !!)