Why does equation 36 in the Chaplygin gas paper need only one boundary condition?

[kptsilva]

Chaplygin gas please help!

Hello every one!

How many of you have learned about the unification of dark energy and dark matter?
I'm doing my research regarding the Chaplygin gas and I've come across this research paper.
arxiv.org/pdf/grqc/0202064.pdf (pls add https:// part)

At the end, they solve the equation 36 (3/2*ab′′ + (1 − w)ab′ − (1 + w)(1 − 3αw)b = 0
, and only use one boundary which is b′(aeq) = 0. Don't we need another boundary condition since this is a second order DE?


Any knowledge will be much appreciated!

 

[member 553083]

Yes, you need two boundary conditions for a second order differential equation. The other boundary condition is usually set with the initial conditions of the system. For example, if you know the initial value of the function b(a) and the initial value of its derivative b'(a) at a certain point a, then you can solve for the constants of integration of the differential equation.