I am interested in numerically integrating a noisy differential equation: $\frac{dx}{dt} = f(x,t) + \epsilon(t)$ where $\epsilon(t) \sim \mathcal{N}(\mu, \sigma^2)$. Is this a RODE or SODE?
How does this relate to numerically integrating $\frac{dx}{dt} = f(x,t)$ using Euler and adding Gaussian noise after each step?