A system of equations $$\frac{df}{dt}(t)=-txg(t)-x, \frac{dg}{dt}(t)=(1-t)xf(t)+x$$ which was constructured from the integral equation $$ F_t (t,x)= x \int_0^{1-t} (1-s)F(s,x) ds + (1-t)x, $$ This generating function comes from some recurrence relation. Is it possible to get (explicitly written) solutions expressed in terms of familiar functions? I guess it won't be easy because the system of ODEs is not an autonomous, that is, time-dependent. Would you give me any suggestions on this?
2026-03-28 20:59:14.1774731554
Can we get a general solution to the following system of equations?
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