a problem with linear system of 4 differential equation

Hi,

the function desolve can solve your initial value problem. View documentation by typing 
? desolve
for more examples. And there is a chapter on differential equations in the manual.

(%i1) display2d:false$
(%i2) eqn_1: 'diff(u(z),z,1)+om(z)=0$
(%i3) eqn_2: 'diff(om(z),z,1)-m(z)/d-(gam^2*p/d)=0$
(%i4) eqn_3: 'diff(m(z),z,1)-t(z)=0$
(%i5) eqn_4: 'diff(t(z),z,1)+p=0$
(%i6) atvalue(u(z),z=0,0)$
(%i7) atvalue(om(z),z=0,0)$
(%i8) sol: desolve([eqn_1,eqn_2,eqn_3,eqn_4], [u(z),om(z),m(z),t(z)])$
(%i9) sol: ratsimp(sol)$

For better readability I omit Maxima's response here. By replacing the $ by ; you'll see the 
answers.

The boundary values you can use to eliminate the unknown m(0) and t(0).

(%i10) bc_1: subst(L,z,rhs(sol[1]))=0$
(%i11) bc_2: subst(L,z,rhs(sol[3]))=0$
(%i12) sol: eliminate(append(sol,[bc_1,bc_2]),[m(0),t(0)])$
(%i13) sol: solve(sol,[u(z),om(z),m(z),t(z)])$

L is introduced. I declare z to be the main variable and simplify. 

(%i14) declare(z,mainvar)$
(%i15) sol: ratsimp(sol)$

I hope you like the result.

Volker van Nek


Am 25 Aug 2008 um 8:26 hat mssivava geschrieben:

> 
> Hi everyone, I have 4 linear system of differential equations which are 
> eqn_1:diff(u(z),z,1)+om(z)=0; eqn_2:diff(om(z),z,1)-m(z)/d-(gam^2*p/d)=0; eqn_3:diff(m(z),z,1)-
> t(z)=0; eqn_4:diff(t(z),z,1)+p=0; My initial conditions are u(0)=0, om(0)=0 My boundary conditons 
> are u(L)=0, m(L)=0 I would like to find u(z), om(z), m(z) and t(z) So, I tried to use desolve 
> function to solve this equation system. But I couldn't. Can anyone help me to solve this system. 
> Thanks in advance
> 
> View this message in context: a problem with linear system of 4 differential equation
> Sent from the Maxima mailing list archive at Nabble.com.
>