# Problems with solving a linear inhomogeneouss ODE system

I am having trouble finding a symbolic solution to the system below:

v[t_] = {Subscript[v, 1][t], Subscript[v, 2][t], Subscript[v, 3][t]}
B = {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}
elc = {Subscript[e, 1], Subscript[e, 2], Subscript[e, 3]}
A = q/c {{0, Subscript[b, 3], -Subscript[b, 2]}, {-Subscript[b, 3], 0,
Subscript[b, 1]}, {Subscript[b, 2], -Subscript[b, 1], 0}}

system = v'[t] == 1/m ( A.v[t]+q elc)
sol = DSolve[system, {Subscript[v, 1], Subscript[v, 2], Subscript[v, 3]}, t]


Note $q,c,B,elc,m$ are all constants (or their components are). The answer I get running the code is very complex/not correct. Any comments on how to improve would be appreciated.

• Why do you think the solution is not correct?
– user44307
Nov 10, 2016 at 19:40

This is more like a long comment.

First, I'm very suspicious about using Subscripts (however, in this case they seem to work quite well), so I changed the symbols used in the code:

v[t_] = {v1[t], v2[t], v3[t]};
B = {b1, b2, b3};
elc = {e1, e2, e3};
A = (q {{0, b3, -b2}, {-b3, 0, b1}, {b2, -b1, 0}})/c;
system = Derivative[v][t] == (A.v[t] + q elc)/m;
sol = DSolve[system, {v1[t], v2[t], v3[t]}, t];


sol is indeed lengthy and rather complicated, yet contains only simple elementary functions; I'd expect FullSimplify to significantly simplify the output:

FullSimplify @ sol


Indeed it produces a much shorter output which is quite comprehensive; the system has a number of constants, so I think this is a reasonable length for its solution: 