>306,313,315
f(x) -1 = a∫_[0,x] f(y)cos(x-y) dy.
f'(x) = af(x)sin(x-x) + a∫_[0,x] f(y)cos(x-y) dy = a∫_[0,x] f(y)cos(x-y) dy.
f"(x) = af(x)cos(x-x) - a∫_[0,x] f(y)sin(x-y) dy = af(x)- a∫_[0,x] f(y)sin(x-y) dy = (a-1)f(x)+1.
これより f(0)=1, f'(0)=0, f"(0)=a.

a<1 のとき f(x) = {1-a*cos[√(1-a)･x]}/(1-a).
a=1 のとき f(x) = (x^2)/2 +1.
a>1 のとき f(x) = {a*cosh[√(a-1)･x] -1}/(a-1).