Question: Deal with Characteristic Roots when solving numerically.

Hi all,

I am doing some research requiring solving a system of differential equations.

When I graph my solutions I sometimes get very strange results (values going to infinity in a time plot). But, with some advice from a friend, I put a negative sign in front of one of the differential equations. Now when I solve, I get the correct result. I am assuming this has something to do with Characteristic Roots, and that when Maple solves these it does not know which roots to use. The negative helps straighten it out. But, using the negatives becomes more cumbersome when I have more than 2 or 3 equations. How is this normally dealt with?

Any help would be much appreciated. I am attaching the code for the 2 ODEs in my example. Is there anyway to get this result without the negatives?

Thanks,

Steve

 restart;
 c0 := 125;
 c1 := -0.35e-1;
 z := -3259;
 v := -.73;
AS := 135000;
m := .1;
d := 470365;
F := 173000;

Eq1 := diff(H(t), t) = (F+v*W(t))/AS;
Eq2 := diff(W(t), t) = -m*W(t)+m*z*c1*H(t)-c1*F*z/AS+m*d+m*z*c0;
print(`output redirected...`); # input placeholder
           
sol1 := dsolve([Eq1, Eq2, H(0) = 3400, W(0) = 448056], numeric, method = rosenbrock);
plots[odeplot](sol1, [t, H(t)], t = 0 .. 2900, color = red);