# Can't Solve a system of differential equations, Solve takes too long

My question is probably not really interesting but I really need help on this because I won't have access to a more powerful computer. So my model contains 7 equations :

dM1dt = (1 - b1) gM M1 ((a11 p DC1/(h11 + p DC1)) + (a12 (1 - q) DC2/(h12 + (1 - q) DC2))) - dM M1;
dM2dt = (1 - b2) gM M2 ((a22 q DC2/(h22 + q DC2)) + (a21 (1 - p) DC1/(h21 + (1 - p) DC1))) - dM M2;
dZ1dt = b1 gZ M1 ((a11 p DC1/(h11 + p DC1)) + (a12 (1 - q) DC2/(h12 + (1 - q) DC2))) - dZ Z1;
dZ2dt = b2 gZ M2 ((a22 q DC2/(h22 + q DC2)) + (a21 (1 - p) DC1/(h21 + (1 - p) DC1))) - dZ Z2;
dDC1dt = 0.5 (ID + (1 - s) dM (M1 + M2) + dZ (Z1 + Z2)) + v1 SC Z1/(k1 + SC) - M1 (a11 p DC1/(h11 + p DC1)) - M2 (a21 (1 - p) DC1/(h21 + (1 - p) DC1));
dDC2dt = 0.5 (ID + (1 - s) dM (M1 + M2) + dZ (Z1 + Z2)) + v2 SC Z2/(k2 + SC) - M1 (a12 (1 - q) DC2/(h12 + (1 - q) DC2)) - M2 (a22 q DC2/(h22 + q DC2));
dSCdt = IS + s dM (M1 + M2) - v1 SC Z1/(k1 + SC) - v2 SC Z2/(k2 + SC);


And I just want Mathematica to give the equilibrium points of this system :

coex = Simplify[Solve[{dM1dt == 0, dM2dt == 0, dZ1dt == 0, dZ2dt == 0, dDC1dt == 0,dDC2dt == 0, dSCdt == 0}, {M1, M2, Z1, Z2, DC1, DC2, SC}]] // MatrixForm


It solved it almost instantaneously for a 4 equations system but it just keeps Running (I tried to leave it run for more than 1 hour) for my 7 equations system, so I can't get the results. Is there a way to simplify or divide the commands?

Thanks a lot in advance.

• Giving values to {gM, a11, a22, ID ..} would help I assume. – Öskå May 20 '14 at 23:40
• Well I was hoping not having to do that to get the analytic result.. – Elsa May 21 '14 at 0:03
• There is like 15 variables, that's way too much. I guess Mathematica can solve it, but that would require ages. – Öskå May 21 '14 at 10:03