In Response To 'Re: Re: DSolve with a set of equations'
If you search this forum for DSolve and then for NDSolve you will see there have been a combined one thousand posts "why can't Mathematica solve this differential equation the way I write it?"
Exactly and precisely what was wrong with the way you wrote that I cannot really tell you. At one point I was getting error messages about one or more of your functions or equations being independent of what you were asking to solve for.
Your original post wasn't asking for any of the other functions that you had written and I started eliminating functions. I also tried asking DSolve to find all the remaining functions, leaving out functions seems to be more likely to cause errors and failures, but that may just be my personal superstition.
With a little experimentation you see what I ended up with.
There are thirty textbooks entirely on the subject of solving differential equations with Mathematica.
Choosing two or three of the best of those and mastering every detail in them might be a good first start.