Differential Equations is really an integration topic.
Find a general solution of a differential equation of the form dy/dx = ... by separating the variables, then integrating to find a general solution (i.e. with a constant of integration).
To be able to solve a differential equation, by finding the general solution and substituting values to find the constant of integration.
To be able to apply the above to contextual problems
Differential Equations
Solving a differential equation
Differential equations in context
This link is to a set of examples, work through them all.