# Question:Integro-differential equation and help solving a system

## Question:Integro-differential equation and help solving a system

Maple

Hi everyone

It's been a while since I last used Maple, so maybe these are simple questions

The first is:

I have a DE

eqbz:=diff(y(x),x)=-l/x^2*(y(x)^2-yeq(x)^2)

yeq(x) is a simple function of x and I want to solve it with "l" as a parameter and ic:=y(0.01)=1

sol:=dsolve({eqbz,ic},numeric,output=listprocedure,range=0.01..10^3,parameters=[l])

then I proceed to plot

ysol:=eval(y(x),sol)

ysol(parameters=[l=x]):

current:=convert(ysol(parameters,`global`):

loglogplot(ysol(x),x=1..100);

This works until l=10^6 or so, when it doesnt plot anymore. Now, I know that there's a solution for higher values of "l" (asked a friend to try on mathematica 8). How to solve this?

The other question is, when I try to use yeq(x) as an integral on a variable different than x

yeq:=x^3*evalf(Int(p^2/(exp(x*sqrt(p^2+1))+1),p=0.001..10^5))

with the same dsolve, I get an error saying there's an extra non-specified variable {p}

I tried to set yeq as a procedure

yeq:=proc(x)

local p

x^3*evalf(Int(p^2/(exp(x*sqrt(p^2+1))+1),p=0.001..10^5))

end proc:

and use dsolve(..., known=yeq) but I get the same error. I had another system where I did it differently:

ydef:=yeq(x)=evalf(Int...))

sys:=subs(ydef,eqbz)

dsolve(sys,...)

again it doesn't work. Any suggestions?

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