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I am somehow confused. What Mathematica means by hashtag within the result for my differential equation?

DSolve[y'[x] + R*y[x] == T* (y[x])^(-1) + R, y[x], x]
{{y[x] -> 
   InverseFunction[
     ArcTan[(Sqrt[R] (-1 + 2 #1))/Sqrt[-R - 4 T]]/(
       Sqrt[R] Sqrt[-R - 4 T]) + Log[T + R #1 - R #1^2]/(2 R) &][-x + 
     C[1]]}}
  • See "What the @#%^&*?! do all those funny signs mean?". It's not a tag, and the octothorp # is (or was) called a pound sign (as in a 50# bag of sand) or number sign (as in the #1 draft pick) in the US, until Twitter used it a special symbol; "hash sign" seems to be chiefly Brit., though again Twitter has spread it around the world, perhaps because the sign has some similarity to hatch marks. – Michael E2 Apr 15 '18 at 12:04

1 Answers1

3

In Mathematica, the hash values are arguments of Function.

From reference:

Function[body]
  or body& is a pure (or "anonymous") function. The formal parameters are # (or #1), #2, etc.

In your case it's #1 and function is:

(Sqrt[R] (-1 + 2 #1))/Sqrt[-R - 4 T]]/(
   Sqrt[R] Sqrt[-R - 4 T]) + Log[T + R #1 - R #1^2]/(2 R) &

Note the trailing &.

m0nhawk
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