To convert complicated differential equations into autonomous equations, introducing a new variable can help eliminate time from the equation. For instance, transforming an equation like (x' - x)t + x = 0 by letting u = xt simplifies it to u' = u. If this method does not work, another approach is to create a system of two equations in two variables, where the second variable represents time. These techniques can facilitate the transition to an autonomous system. Understanding these methods can aid in solving complex differential equations effectively.