Question: How to solve the system algebraically?

In the system below, I need to solve the solution algebraically (it is known in advance that from "V3" that a0=1,just open the V3 command).

V := exp(lambda*S) = S^4*a4 + S^3*a3 + S^2*a2 + S*a1 + a0;
V1 := subs(S = 2, V);
V2 := subs(S = 1, V);
V3 := subs(S = 0, V);
V4 := subs(S = -1, V);
V5 := subs(S = -2, V);
fsolve(subs(a0 = 1, {V1, V2, V4, V5}), {a1, a2, a3, a4});

I already know the answers, but I need maple to provide me with the command in the form

a1:=(1/6)*[8*sinh(lambda)-sinh(2*lambda)] and


a3:= ... etc.

What is the best way to do this?

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