How to solve a stochastic differential equation?

Question

This is a stochastic differential equation,

$$ dx(t) = -x(t)dt + e^{(-t)} dw(t)$$

I am not able to determine the next steps to solve this equation.

Answer 1

Something like this?

procx = ItoProcess[\[DifferentialD]x[t] == 
    x[t]*\[DifferentialD]t + Exp[-t]*\[DifferentialD]w[t], 
   x[t], {x, 0}, t, {w \[Distributed] WienerProcess[]}];

datax = RandomFunction[procx, {0, 5, 0.1}, Method -> "StochasticRungeKutta"];

ListLinePlot[datax]