I am preparing myself for a post undergraduate (masters) entrance exam in mathematics. Can someone suggest a really good practice material with challenging questions of all types for ordinary differential equations (any order/homogeneous/non-homogeneous etc.)? Do you think Differential Equations - Martin Braun useful for this purpose? I don't want any elementary text as I already have it, I think a good practice material would be more useful..
It is hard to advice some book. Because differential equations are either easy to solve (these equations are in undergrauate textbooks) or difficult. When I studied mathematics we over in undergraduate course all types of ODEs, but solution of them was mainly "mechanical work". Difficult nonlinear equations are solved by numerical methods. So maybe you can go in this way. You can also look at some applications of ODE, there you can find difficult problems...equations with uncertain data, control theory, dynamical systems, biomathematics. In textbooks of ODEs are mainly basic exercices but problems from practice can be extremely tough (my experience from industry). Try to look at some textbooks in this fields, there could be more difficult problems. I have job as mathematician for industry and sometimes find solution of some problem is not easy exercise.