Assigning Solve Solutions in Mathematica

This can be quite tricky, first define a system of equations:

ClearAll["Global`*"]
 
eq6a = x'[
    t] == g * (y[t] Subscript[b, z][t] - 
       z[t] Subscript[b, y][t]) - Subscript[R, 2] x[t];
eq6b = y'[
    t] == g * (z[t] Subscript[b, x][t] - 
       x[t] Subscript[b, z][t]) - Subscript[R, 2] y[t];
eq6c = z'[
    t] == \[Gamma] * (x[t] Subscript[b, y][t] - 
       y[t] Subscript[b, x][t]) - 
    Subscript[R, 1] (z[t] - Subscript[M, 0]);

Use the solve command to solve it:

Solve[{eq6a, eq6b}, {x[t], y[t]}]

If that works use substitution to grab one of the variables, say $x(t)$ :

s = First[x[t] /. Solve[{eq6a, eq6b}, {x [t], y [t]}]]

You'd think that you could just perform xfunc[t_] = s but that WILL NOT work, instead you have to do a re-substitution in order for it to grab the value:

xfunc[blah_] := s /. t -> blah
xfunc[t]

• WARNING

  • The function name, as above xfunc[] MUST NOT be x[t] otherwise there will be some sort of recursive error and Mathematica will time out

    • Be mindful if this occurs, it is not-sufficient to use Alt + . , or to kill the kernel from the memory, Mathematica MUST be restarted because it will behave strangely.

    So doing this all together:

    Solve[{eq6a, eq6b}, {x [t], y [t]}];
s = First[x[t] /. Solve[{eq6a, eq6b}, {x [t], y [t]}]];
vfunc[blah_] := s /. t -> blah
vfunc[t]

paperclipCheck out this Example: