Differential Eqs on GRE Math Subject Exam

[snipez90]

Hi, does anyone know the extent to which differential equations are tested on the GRE Math Subject test? I basically looked at Princeton Review's review, and reminded myself of the following:

-Basic DE's (immediate integration)
-Solutions to f' = f, y'' + y = 0
-Separable DE's
-Homogeneous equations (the function is homogeneous)
-Exact equations
-Using integrating factor for non-exact equation (so I only know two types of integrating factors in this case, namely when (M_y - N_x)/N is a function of x alone and a similar case, where the DE is M*dx + N*dy = 0 and subscripts denote partial derivative wrt that variable)
-First-Order Linear Eqs.
-Higher-Order Linear Eqs. w/ Const. Coefficients

I have not taken a formal course on differential equations and most of what I know came from looking at http://www.sosmath.com/diffeq/diffeq.html" a long time ago (mostly first order stuff, and I've forgotten certain variants such as Bernoulli).

Am I overlooking a certain type of equation? As much as I'd like to spend more time on DE's, I need to spend more time on algebra and multivariable calculus, so I want to have an idea of which equations are most likely to show up. Thanks.

 

[TonyG]

Hello!

I can tell you that differential equations are an important part of mathematics and are often used in various scientific fields to model and solve problems. On the GRE Math Subject test, differential equations are usually tested in the Calculus section and make up about 10-15% of the questions.

Based on your list, it seems like you have a good understanding of the different types of differential equations that may appear on the test. However, I would also recommend reviewing and practicing with higher order linear equations with non-constant coefficients, as well as systems of differential equations. These are two commonly tested topics that may not have been covered in your self-study.

Additionally, it is important to have a strong understanding of the fundamental concepts and techniques used in solving differential equations, such as separation of variables, integrating factors, and initial value problems. Make sure to review these thoroughly and practice solving a variety of problems.

Overall, the best way to prepare for the GRE Math Subject test is to have a solid foundation in calculus and practice solving various types of differential equations. Good luck on your test!