The book Cracking the GRE Mathematics Subject Test, 4th Edition (Graduate School Test Preparation) should be sufficient.http://www.amazon.com/Cracking-Mathemat ... 0375429727
For even more in-depth books on differential equations, you can check out textbooks, especially those with the part on existence and uniqueness theorems, like G. Simmons, Differential Equations with Applications and Historical Notes, 2nd Ed., McGraw-Hill.
UCLA uses the above book. (http://www.math.ucla.edu/ugrad/courses/ ... line.shtml
Hope it helps.