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I am interested in solving the following type of system of differential equations for η(x):

(1) ∫η(x)ω(x)=0

(2) ∫η'(x)ω(x)=0

for known ω(x), and known limits of the integral. Does this type of equations have a name? Can someone help me to find some reference? Thanks a ton!

Cheers,

Kev