Dear Mr Paul,
You have asked a good question, and I will try and assist you as much as I can.
It is important that you complete the form fully and accurately as this helps the authority to decide the application swiftly.
If however, you are unable to provide the infirmation requested, such as your ex-wife's DOB, then you can leave this blank and put in a covering letter with your application explaining why you are unable to provide this information. This way, the decision maker will understand why you left this information blank in the form.
I do not anticipate any issues.
I hope you have had a chance to look at my response.
Any queries, please let me know, otherwise please kindly rate my answer.