Hello Math Help Forum! This is my first time posting.

I am currently working to understand a derivation that involves a similarity solution and there is one step that I am stuck on. In this step, one of the governing equations is transformed into a new equation based on the new variables. However, when I insert the new variables into the governing equation, I am unable to produce the transformed equation.

I have attached a .pdf file called "ProblemStatement" in which I explain the step that has me stuck.

I have also attached a .pdf file called "ProgressSoFar" in which I outline the attempt that I have made so far. I am hoping that I am close--that there is just something that I am not seeing--and that it will not be too much work for someone to pick up from where I have left off. However, I have made two separate files because I don't want to get anyone started off on the wrong foot if I have gone about this all wrong.

Thanks for your help!