Re: [Maxima-discuss] how to solve a differential equation defined by differentials?

[Michel T. <ta...@lp...>]

Ode2 expects a differential equation in ordinary form. So  "divide by 
dm". The documentation

for ode2 says that it knows how to use the method of separation of 
variables.


(%i1) declare(cp,constant);

(%o1) done
(%i2) declare(cv,constant);

(%o2) done
(%i3) ode2(cv*m*'diff(T,m)+(cp+cv)*T=0,T,m);

(%o3) T = %c*%e^-(((cv+cp)*log(m))/cv)

Le 02/02/2023 à 19:41, fi...@ig... a écrit :
> Dear Maxima Users,
>
> in physics we often have problems which can be expressed in
> differentials, like this simple example (it describes gas flow from a
> leak in a pressure vessel)
>
>     declare([cp, cv], constant);      /* heat capacity         */
>     u : cv * T;                       /* spec. internal energy */
>     h : cp * T;                       /* spec. enthalpy        */
>     U : m * u;                        /* internal energy       */
>     E : diff(U) = -h * diff(m);       /* energy conservation   */
>
> (%o5)              cv T del(m) + cv m del(T) = - cp T del(m)
>
> %o5 is actually a differential equation in T and m. It can easily be
> solved by separation of variables - but how to do this using Maxima?
>
> Actually: how could it be solved using ode2() or how can it be
> transformed such that ode2() can solve it?
>
>
> Thanks and best regards
>
>
> Torsten
>
>
>
-- 
Michel Talon