Question: Making a function from solve or dsolve results

How can I make a function from the results of equation (4) in the below image from the attached file? As seen in equation (6) my attempt at doing this didn't work because it didn't evaluate to a number like equation (7) did.

I saw posts on using numeric results from solve, but I don't see how to use the equation results to make a function of x.

using_solved_equations.mw

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