Subject: Trouble solving system of differential equations
From: Marcelo Costa
Date: Thu, 07 Mar 2013 16:24:16 +0000
Hello,
I have the following program that consists in solving a
system of 6 differential equations:
> ratprint: false$
> realonly:
true$
> display2d:false$
>
> /* eqs */
>
>
eq1:'diff(T1x(x),x)-1037*g(x)=0$
> eq2:'diff(V1x(x),x)-3014*e(x)=0$
>
eq3:'diff(M1x(x),x)-(V1x(x)-1141*g(x))=0$
>
eq4:'diff(K(x),x)-((3/100)-(7/1000)*x-(65/1000000)*M1x(x)-(715/10000000)*T1x(x))=0$
>
eq5:'diff(g(x),x)-((95/1000000)*T1x(x)-(3/100)+(7/1000)*x)=0$
>
eq6:'diff(e(x),x)-(K(x))=0$
>
> /* BVPs */
>
>
atvalue(T1x(x),x=0,600);
> atvalue(V1x(x),x=0,-21);
>
atvalue(M1x(x),x=0,-350);
> atvalue(T1x(x),x=25,0);
>
atvalue(V1x(x),x=25,0);
> atvalue(M1x(x),x=25,0);
>
atvalue(g(x),x=0,k1);
> atvalue(e(x),x=0,k2);
> atvalue(K(x),x=0,k3);
>
> /* solution */
>
> sols:desolve([eq1,eq2,eq3,eq4,eq5,eq6],[T1x(x),
V1x(x), M1x(x),K(x),g(x),e(x)])$
> sols:ratsimp(sols);
I then have 6
solutions, one for each variable as expected. But 4 of the equations
returned include ilt() - inverse laplace transform - which stops me from
using them and calculating the constants k1,k2 and k3 I need.
In
reality I can find k1, because the first solution returned doesn't
contain ilt(), so I can manipulate it with the appropriate BVPs to
determine k1 (which is g(0)), but for the others I can't do that because
of ilt().
What can I do ?
Thank you all,
Marcelo Costa