autoregressive error in solving ordinary differential equations

[hvganesh]

Hi,
Could anyone please help me code the following model in SAS? In essence, I am trying to incorporate autoregressive error in an ordinary differential equation.

x_dot_t = (N - x_t) * (theta1 + theta2 * x_t) + e_t

e_t = rho * e_t-1 + u_t

The code without the autoregressive error is:

proc model data=test;
params theta1 theta2 N;
dert.x = (N-x)*(theta1+theta2*x);
fit x/time=t dw;
run;

I have tried the following and none of them works:

1. %ar(dert.x,1),
2. dert.x = (N-x)*(theta1+theta2*x) + zlag1(dert.x-(N-x)*(theta1+theta2*x));

Thanks in advance for your help.