what i have in mind is,

you first abitrarily set a0, a1,a2,a3,c0,c1,c2,c3,c4 to a random number and call a iteration (if Maple has one) function that can vary these variables to make the RHS of the equation matches up with the RHS. let's say: set a0=1,a1=1.5,a2=1.2,a3=0.5 and so on. just something random and then determine their values.