Some ideas for particular solutions? How to make two Wronskian?

a1*x''''[t] + b1*x''[t] + c1*y''''[t] + d1*y''[t] + e1*y[t] == f1[t],

a2*y''''[t] + b2*y''[t] + c2*x''''[t] + d2*x''[t] + e2*x[t] == f2[t],

All constants are known: a1, b1,...

(Headbang) (Crying)