I have a general question with regard to using stan to solve ODE problems. In the simple harmonic oscillator example, both y[1] and y[2] are supplied during the model fitting. In case of when only one variable can be observed (i.e. only y[1] is known), how should the code by modified in order to model the system? Can you put the whole variable in the parameters chunk and how would achieve that? A lot thanks!

```
functions {
real[] sho(real t, real[] y, real[] theta, real[] x_r, int[] x_i) {
real dy1_dt = y[2];
real dy2_dt = -y[1] - theta[1] * y[2];
return { dy1_dt, dy2_dt };
}
}
data {
int<lower = 0> T;
real t0;
real<lower = t0> ts[T];
real y_hat[T, 2];
real y0[2];
}
transformed data {
real x_r[0];
int x_i[0];
}
parameters {
real theta[1];
real<lower = 0> sigma;
}
transformed parameters {
real y[T, 2] = integrate_ode_bdf(sho, y0, 0.0, ts, theta, x_r, x_i);
}
model {
sigma ~ normal(0.1, 0.1);
theta ~ normal(0.15, 0.1);
y0 ~ normal({1.0, 0.0}, 0.1);
y_hat[, 1] ~ normal(y[, 1], sigma);
y_hat[, 2] ~ normal(y[, 2], sigma);
}
generated quantities {
}
```