This section defines (again; because it was already subject of MS221, I think):

• differential equation
• order
• solution

It also introduces the expression . The margin note says that it is "strictly speaking ... an abuse of notation", because it is not clear what the y stands for: on the left-hand side it is a variable, but on the right hand side it is a function. The margin note also says "it is a very convenient abuse". But why do we use it? Is it really necessary to use this? I find it quite confusing and "all others do use it too" isn't a satisfactory explaination for me?!

Further the terms general solution and particular solution  are defined (again) and in this context, also, the definition for initial condition, initial values and the initial-value problem are defined.