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Question: How to avoid a singularity

Question:How to avoid a singularity

patient 35
dsolve singularity
October 29 2015
0

Hi all,

I deal with the following ODE system which present a singularity when v(x)=0. I want to inject the condition "if v(x)=0 then u(x)=0" as may be a solution to avoid this singularity. If someone could help me to do that. Thanks.

SYS:={u(x)*sqrt(v(x))-diff(v(x),x)*x-2*v(x)=0,2*u(x)*v(x)*diff(v(x),x,x)-u(x)*(diff(v(x),x))^2+2*diff(u(x),x)*v(x)*diff(v(x),x)+v(x)*sqrt(v(x))*(2*x*diff(u(x),x)+6*u(x))=0};

ICS := { u(-2) = 4,   v(-2) = 4, (D(v))(-2) = 0 };
p:= dsolve( SYS union ICS,method=rkf45_dae,numeric,output=listprocedure);
solp := plots[odeplot](p, [[x, u(x)],[x, v(x)]], x = -5 .. 0);
plots[display](solp);
Please Wait...