Exercises identifying types of differential equations

Question

I am preparing for a test and want to know if I can identify the different types of differential equations. Are there any tests online? I have searched but couldn't find any exercises of this type.

Answer 1

There is a big number of different families of differential equations, so other than general advice there is probably not a lot one individual resource/person will do for you. You should probably make sure you are familiar with general properties of Differential Equations, such as order, degree, etc. (you can find such definitions with a simple Google search). You also have

(1) Ordinary Differential Equations (judging by the tags, this is the one you are interested in), where the equation has one independent variable. Some examples include:

(.) Separable ODEs

(.) First Order Linear ODEs

(.) First Order Homogeneous ODEs

(.) Second Order Linear Constant Coefficient Homogeneous ODE

(.) Second Order Linear Homogeneous (not necessarily constant coefficient) ODE

(.) Exact ODE

And many, many more. These are just some that pop to mind straight away, with relatively nice solution methods (apart from non constant coefficient second order linear homogeneous ODE, not necessarily nice to solve).

(2) Partial Differential Equations. Where we have more than one independent variable. Again, there are lots of different types, and the methods of solution tend to be quite different (quite a simple method of solution being something like separation of variables, in which we reduce the problem to a system of ODEs).

Ultimately, Differential Equations are much harder to solve than equations you have probably previously encountered, and most in fact do not have nice solutions. This is why we like to characterize them - it allows us to place names to things we can solve, and what we readily have methods available for.