Autonomous DEs

DEs that have the form

Functions where the rate of change of $y$ depends directly upon only $y$ itself

If any independent variables appear on the right-hand side, the DE is not autonomous

If the derivative at the equilibrium solution, $f^{\prime }(a)>0\to y=a$ is unstable, $f^{\prime }(a)<0\to y=a$ is asymptotically stable

Direct Integration