Dark Energy

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Hello my friends

I have a problem with initial condition for below system of differential equation

sys := {6*(diff(a(t), t))^2+12*a(t)*(diff(a(t), t$2))-3*a(t)^2*phi(t)^(-2*c)*sqrt(1-alpha*(diff(phi(t), t))^2), 2*c*a(t)^3*phi(t)^(-2*c-1)*sqrt(1-alpha*(diff(phi(t), t))^2)-3*alpha*a(t)^2*phi(t)^(-2*c)*(diff(a(t), t))*(diff(phi(t), t))/sqrt(1-alpha*(diff(phi(t), t))^2)-alpha*a(t)^3*phi(t)^(-2*c)*(diff(phi(t), t$2))/sqrt(1-alpha*(diff(phi(t), t))^2)+2*c*alpha*a(t)^3*phi(t)^(-2*c-1)*(diff(phi(t), t))^2/sqrt(1-alpha*(diff(phi(t), t))^2)-alpha^2*a(t)^3*phi(t)^(-2*c)*(diff(phi(t), t))^2*(diff(phi(t), t$2))/(1-alpha*(diff(phi(t), t))^2)^(3/2), R(t) = 6*((diff(a(t), t))^2/a(t)^2+(diff(a(t), t$2))/a(t)), W(t) = -phi(t)^(-2*c)*sqrt(1-alpha*(diff(phi(t), t))^2)/(1/a(t)^3+a(t)^3+phi(t)^(-2*c)/sqrt(1-alpha*(diff(phi(t), t))^2))}

I set {c,alpha}={1,1} but initial conditon is problem ... since I got the following message from maple to illustrate diagrams of W(t), a(t) and even phi(t)

Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up
 

please help me.

 

with the best regard

 

hello my friends

I have a critical problem to solve below the system of differential equations

-(9/14)*R(t)^(19/14)-(285/196)*(diff(R(t), t, t))/R(t)^(9/14)+(2565/2744)*(diff(R(t), t))^2/R(t)^(23/14) = -k*(4*lambda+1/a(t)^3)

and R(t) = 6*((diff(a(t), t))^2/a(t)^2+(diff(a(t), `$`(t, 2)))/a(t))

I need to find form of a(t) numerically from set of differential equatios

plz help me as soon as possible

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