Probably a pretty simple question but I've been stumped for awhile looking around. I'm trying to solve four diff. eq.'s using DSolve and some of these equations depend on a function B[t] which I try to define before using it in DSolve. I'm sure my problem has to do with this B[t] function but I'm too new to Mathematica to know what to do. Here's my code:
bZero = 1575.0
bOne = 0.28
u = 0.02
a = 1/0.0279
g = 1/0.01
B[t_] = (bZero*(1 + (bOne*Cos[2*Pi*t])))
DSolve[{(u - (B[t]*Inf[t]*S[t]) - (u*S[t])) ==
S'[t], ((B[t]*Inf[t]*S[t]) - ((a + u)*Expo[t])) ==
Expo'[t], ((a*Expo[t]) - ((g + u)*Inf[t])) ==
Inf'[t], ((g*Inf[t]) - (u*R[t])) == R'[t]}, {S[t], Expo[t], Inf[t],
R[t]}, t]
And the output:
DSolve[{0.02 - 0.02 S[t] -
1575. (1 + 0.28 Cos[2 \[Pi] t]) Inf[t] S[t] ==
Derivative[1][S][t], -35.8623 Expo[t] +
1575. (1 + 0.28 Cos[2 \[Pi] t]) Inf[t] S[t] ==
Derivative[1][Expo][t],
35.8423 Expo[t] - 100.02 Inf[t] == Derivative[1][Inf][t],
100. Inf[t] - 0.02 R[t] == Derivative[1][R][t]}, {S[t], Expo[t],
Inf[t], R[t]}, t]
Something just isn't working. It's not popping up any errors or anything. I realize it's probably a simple question, but any help is appreciated. Thanks!