25 July 2009
I am not able to find the general function that integrates the following 2nd order differential equation;
y^2 y’’ + 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 constants a and b.
I would be deeply grateful to any friend who can help me resolve the problem.
Many thanks for any help.