Gsoc'16: Adding new methods for solving ODE's

[Abhishek kumar]

Hi,

I am Abhishek kumar  and i want to work on the ODE's(https://github.com/sympy/sympy/wiki/GSoC-2016-Ideas#ordinary-differential-equations) project through Gsoc'16. I have completed course on Differential Equations.

I code in c/c++ and python.

I went through https://github.com/sympy/sympy/blob/master/sympy/solvers/ode.py and found that most of the mothods for solving 1st order 

ODE's are implemented.

So,I think it would be better to start with 2nd order ODE's:

I want to add on these topics to dsolve( ):

1. Solving Differential Equations in Terms of Bessel Functions.

2. Lie Group method for solving second order ODE's.

3. Solving System of ODE's.

I want to know that is this good to start with these topics.

Thanks.