I want so solve the following SDE
\begin{align}\dot{y}(t)=r(t)y(t)+\epsilon_1(t) \\ \dot{r}(t)=r(t)+\epsilon_2(t)\end{align}
with $r,y$ both being stochastic processes and $e_1,e_2$ both being gaussian white noise processes with variance $\sigma^2_1$ and $\sigma^2_2$ respectively. A gaussian white noise process is a gaussian process with mean function $m(t)=0$ and kernel function $k(t,t')=\delta_{tt'}\sigma^2$, where $\delta_{ij}$ is the kronecker delta. $\sigma^2$ is called variance of the gaussian white noise process.
I think an alternative problem description using wiener processes (Brownian motion) would be
\begin{align} dy(t)=r(t)y(t)dt+\sigma_1dW_1(t) \\ dr(t)=r(t)dt+\sigma_2dW_2(t) \end{align}
where $W_1$ and $W_2$ are wiener processes.
I don't have any background in solving stochastic differential equations. Thus, my approach so far has been trying mathematica, which was not too successful yet.