.Hey,

   My proposal is also going to be in the same area (Ordinary Differential 
Equations), I am going to deal with the implementation of series solutions 
and solving of first order equations using Lie groups. As far as I know, 
there are many other topics also given under differential equations in the 
sympy wiki. 

All the best to you, and I hope both of us get selected :-)

2. Ordinary Differential Equation.
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