Question:ode system problem

Question:ode system problem

Maple

I try to solve a nonlinear ode system. in numerical calculation it always calcualte the second derivative of my variable zero, while in the plot of the first derivative on the variable it shows that the second derivative has not to be zero

here is my problem:

My variables are a(t), phi(t). Bty solving the system of ode1 and ode2 and plotting a(t) and its first and second derivateive we see that its second derivative is always zero whime from the graph af its first derivative it has not to be zero.

> restart;

> with(plots);

> b := 0.5e-1; f0 := 0.5e-1;

> with(PDEtools, casesplit, declare);

> with(DEtools, gensys);

> declare((phi, H, f, a)(t));

> H := proc (t) options operator, arrow; (diff(a(t), t))/a(t) end proc;

> H1 := diff(H(t), t);

> R := 12*H(t)^2+6*H1;

> f := proc (t) options operator, arrow; f0*exp(b*phi(t)) end proc;

> f1 := (diff(f(t), t))/(diff(phi(t), t));

> phi1 := diff(phi(t), t); phi2 := diff(phi1, t);

> rho := (1/2)*phi1-3*H(t)*f1*phi1;

> ode1 := phi2+3*H(t)*phi1+R = 0;

> p := -(diff(diff(f(t), t), t))-2*H(t)*(diff(f(t), t));

> ode2 := -p = 2*H1+3*H(t)^2;

> sys := {ode1, ode2};

ics := {a(0) = 1.0, phi(0) = 0.1e-1, (D(a))(0) = 0, (D(phi))(0) = 2.};

dsol := dsolve(`union`(sys, ics), numeric, stiff = true);

> odeplot(dsol, [[t, a(t)]], -50 .. 50, numpoints = 10000, color = black);

> odeplot(dsol, [[t, diff(a(t), t)]], -50 .. 50, numpoints = 10000, color = black);

> odeplot(dsol, [[t, diff(a(t), `\$`(t, 2))]], -50 .. 50, numpoints = 10000, color = black);

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