Using dimensional analysis to create dimensionless equation

[astrofunk21]

Homework Statement

I am tasked with solving and creating a dimensionless equation from a differential equation given.

Homework Equations

This is the given equation:

The Attempt at a Solution

When doing the dimensional analysis I see that we are left with units of [m^-3][kg¹][s^-2].

These units are actually the units of the inverse of the gravitational constant G. So to make this equation dimensionless would I just multiple both sides by G? So we get this dimensionless equation (but not really since the left side isn't exactly dimensionless):

Would appreciate help on where to go with this! Thanks in advance

 

[Orodruin]

Please give the problem exactly as stated.

 

[astrofunk21]

Please give the problem exactly as stated.

Question: Solve and make a dimensional analysis in order to ensure the equation is really dimensionless.

 

[Orodruin]

That is not the entire problem. It sounds like the very end of the problem text.

 

[Chestermiller]

What is c in the equation?