25 July 2009

I am not able to find the general function that integrates the following 2nd order differential equation;

y^2y’’ + a y^3 –b =0

in which 0 ≤a≤ 1 is a constant;

b>0 is a constant.

The equation relates to the behaviour (orbit/motion) of a massless point subjected to a particular central motion.

I could easily find only the solutions associated with nil values for constantsaandb.

I would be deeply grateful to any friend who can help me resolve the problem.

Many thanks for any help.

Leo Klem