Question: system of ODEs HDEDGP

Dear guys!

I want to solve this system:

> c := 1: RC := 0.03: h := 1: m := 0.3:

> a := H(z)^2/(1+z)-h^2*(m*(1+z)^2+2*RC/(1+z));

> ode1 := diff(H(z),z) = (H(z)^4/((1+z)^2)+m*(1+z)*h^2*H(z)^2-2*m^2*h^4*(1+z)^4)/(2*H(z)*a) - (2*H(z)*h^2*RC)/(a*(1+z)^2) + (2*RC*h^2*(1+z)/(c*H(z)^2*a))*(H(z)^2/(1+z)^2-(H(z)^2/(1+z)-m*h^2*(1+z)^2)^2/(4*RC*h^2))^(3/2):

> ode2 := diff(M(z),z)=3*M(z)/(1+z)-2*M(z)*diff(H(z),z)/H(z):

> sys := {ode1, ode2}:

> ics := {H(0) = h, M(0) = m}:

> sol := dsolve(`union`(sys, ics), numeric, output = listprocedure, stiff=true);

but I recieve the error: Error, (in dsolve/numeric/SC/firststep) unable to evaluate the partial derivatives of f(x,y) for stiff solution

Does anybody know what the problem is? And how can I solve my system?

To solve the problem I removed the term "stiff=true". Apparently it works but when I want to specify the value of H or M in a special z I get a new error:

> HH, MM := op(subs(sol, [H(z), M(z)]));

> MM(2);

 Error, (in MM) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

(Also for HH(0.5) the same error) 

What should I do? Have I solved my first problem right? And how can I solve the new problem?

Thank you

 

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