Hello Jean,
Why don't you use stiff solvers, for example from DotNumerics plugin. They will cope with this equations well (dn_AdamsMoulton, dn_ExplicitRK45, dn_GearsBDF..).

Regards,
Radovan
P.S. By the way, uni made many ode solvers in few plugins, and I think SMath is very good regarding ODE solvers
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"