I am trying to find a closed-form (analytical) solution for the two following simultaneous integro-differential equations :(adsbygoogle = window.adsbygoogle || []).push({});

du[x]/dx= - a v[x] +b ∫〖[1-(y-x)^4 〗].(v[y]-v[x])dy

And

(dv[x])/dx= - f u[x] -g ∫〖[1-(y-x)^4 〗].u[y]dy

With the initial conditions:

v[0]=e and u[1]=0

a,b,f,g and e are positive constants

Both integrals are from y=0 to y=1.

The unknowns are u[x] and v[x].

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# A Solving two simultaneous integro-differential equations

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