what is the solution for y in this peculiar ODE ?

with initial conditions :

moreover

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- Dec 31st 2009, 06:02 PMmmzaja peculiar ODE
what is the solution for y in this peculiar ODE ?

with initial conditions :

moreover

- Jan 1st 2010, 06:33 AMchisigma
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

- Jan 1st 2010, 06:34 PMmmzaj
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 !!)