A way to implement this is Dynamic programming - using a dictionary/corpus to compare your individual words against(and also the left over words after you have parsed the text into strings).
Think of it like you were writing a custom spell-checker or likewise. In this, there's also a scenario when more than one combination of words may be left over eg -"walkingmydoginrain" - here you could break the 1st word as "walk", or as "walking" , and this is the beauty of DP - since you know (from your corpus) that you can't form legitimate words from "ingmydoginrain" (ie rest of the string - you have just discovered that in this context - you should pick the segmented word as "Walking" and NOT walk.
Also think of it like not being able to find a match is adding to a COST function that you define, so you should get optimal results - meaning you can be sure that your text(un-separated with white spaces) will for sure be broken into legitimate words- though there may be MORE than one possible word sequences in that line(and hence, possibly also intent of the person seeking this)
You should be able to find pretty good base implementations over the web for your use case (read also : How does Google implement - "Did you mean" )
For now, see also -
How to split text without spaces into list of words?