Existence and Uniqueness - Using the existence-uniqueness theorem show that the following IVP has a solution but it is not unique:
y''+y'/x-9y/x^2=0
y(0) bounded
general solution: y=Ax^3+Bx^{-3}
Initial Value Problem - I am looking for the solution of this problem. It involves a little bit of theory in the second part. In the solution give a detailed solution showing all assumptions and theorems.
Uniqueness of a Reflector - Show that if Qx=y, where Q= I- ruu^T (r can be denoted as gamma) , then u must be a multiple of x-y. In other words, prove the uniqueness of reflector Q.