ode system is singular at the initial point

Question:ode system is singular at the initial point

Posted: Dkunb 65 Product: Maple 2021

April 13 2023

Could you help me how to deal with this problem?

restart;

>	with(plots):with(plottools):with(DETools):

>	Sys:=diff(T(R),R)=((1-1/R)(sqrt(1-(alpha/R)^2(1-1/R))))^(-1),diff(Phi(R),R)=(alpha/R)^2(sqrt(1-(alpha/R)^2(1-1/R)))^(-1);

diff(T(R), R) = 1/((1-1/R)*(1-alpha^2*(1-1/R)/R^2)^(1/2)), diff(Phi(R), R) = alpha^2/(R^2*(1-alpha^2*(1-1/R)/R^2)^(1/2))

(1)

>	inits:=[[T(0)=0.5,Phi(0)=0],[T(0)=0.5,Phi(0)=Pi/4]];

(2)

>	K:=dsolve([Sys,op(op(1,inits))],[Phi(R),T(R)],numeric,parameters=[alpha],output=listprocedure);

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