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Question: How do I solve an intgro-differenetial equation numerically

Question:How do I solve an intgro-differenetial equation numerically

isifesai 30 Maple
integration differential-equation numeric integro-differential-equation
August 20 2018
3

Good day all, I have a yet challanging integration problem. The problem is to find the numerical solution of the problem:
Eq1 := x(t) = x(b)+c*t+k*x(b)*t-k*(int((t-s)*x(s), s = 0 .. t))+2*(int(sqrt(t-s)*x(s)^3, s = 0 .. t))/sqrt(Pi)

I differentiated Eq1 wrt x as follows:Eq2 := diff(Eq1, t)

Lastly, on typing sol := dsolve({Eq2, x(0) = x(b)}, x(t), numeric)

I got an error messag. Please all the valuable suggestions given to me on a similar problem could not solve this one as this appears to be a little complex when compared to my previous question. Please I need your help. Thanks

 

 
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