# Stochastic differential equation problem

## Main Question or Discussion Point

Sorry if this is in the wrong section but i have a problem, I have no experience with stochastic equations well analytically anyway.

The equation i have is the following;

$\frac{dv}{dt} = - \alpha v+ \lambda F+\eta$

Where alpha lambda and F are constants, v is a variable (speed in this case) and eta is a random value. I believe this is similar to Brownian motion with an applied field, although i have no idea how to solve this analytically i plan to solve it analytically and compare it to a numerical solution. So any help will be most appreciated!