You have a couple of issues. Unfortunately, even after fixing them I
was unable to get a solution from SymPy.
First, u0 is already u^0(tau). You do not need to call u0(tau) again.
Second, you have a typo. You wrote
u3=Function('u^0')(tau)
instead of
u3=Function('u^3')(tau)
I fixed these but I hit another issue that looks like a bug in SymPy
UnboundLocalError: local variable 'eq_no' referenced before assignment
It seems dsolve() doesn't like the use of dynamicssymbols. You should
replace dynamicssymbols('tau') with a regular symbols() object for the
call to dsolve as a workaround.
I did this but then dsolve just hung and eventually returned None. So
this is a bug in SymPy.
Aaron Meurer
On Fri, Jan 13, 2017 at 12:33 PM, 'frank zack' via sympy
<[email protected]> wrote:
> How can I solve a system of ode's?
>
> That's what I've tried:
>
> from sympy import *;
> init_printing()
>
> Ex,Ey,Ez,Bx,By,Bz,c,m0,t,u,we,wb,q=symbols('E_x E_y E_z B_x B_y B_z c
> m_0 t u omega_E omega_B q')
> tau=dynamicsymbols('tau')
>
> u0=Function('u^0')(tau)
> u1=Function('u^1')(tau)
> u2=Function('u^2')(tau)
> u3=Function('u^0')(tau)
>
> u=Matrix([u0,u1,u2,u3])
>
> Emat=Matrix([[0,Ex/c,Ey/c,Ez/c],[Ex/c,0,Bz,-By],[Ey/c,-Bz,0,Bx],[Ez/c,By,-Bx,0]])
> RHS=q/m0*Emat*u
>
>
> odesys=[Eq(u0.diff(),RHS[0]),Eq(u1.diff(),RHS[1]),Eq(u2.diff(),RHS[2]),Eq(u3.diff(),RHS[3])]
> odesys
> dsolve(odesys,[u0(tau),u1(tau),u2(tau),u3(tau)])
>
> Unfortunately it gives me a TypeError:
>
> TypeError Traceback (most recent call
> last)
> <ipython-input-94-f4af1f7e485c> in <module>()
> 16
> odesys=[Eq(u0.diff(),RHS[0]),Eq(u1.diff(),RHS[1]),Eq(u2.diff(),RHS[2]),Eq(u3.diff(),RHS[3])]
> 17 odesys
> ---> 18 dsolve(odesys,[u0(t),u1(t),u2(t),u3(t)])
>
> TypeError: 'u^0' object is not callable
>
> I've tried so many things, but I just can't figure out the proper syntax for
> this to work.
> Any ideas?
>
>
> BTW: It doesn't help if I use dynamicsymbols instead of functions:
>
> ...
> dsolve(odesys,[u0(tau),u1(tau),u2(tau),u3(tau)])
> ...
> dsolve(odesys,[u0(t),u1(t),u2(t),u3(t)])
>
> -> Same TypeError
>
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