Both of these expressions mean "I don't know", and as they are, they may be used interchangeably. I would also agree with Kevin that “ewan ko” (sometimes spelled as “aywan”) is more colloquial/informal, but it may also depend on the manner by which it is expressed. “Hindi ko alam” is the actual translation of “I don’t know”. On the other hand, I think “ewan ko” is like an idiomatic phrase in the sense that this expression is only used in that way. It is also almost always used in the first person that if you say only “ewan” (which is even more informal), it would be the same as saying “ewan ko”. We don’t really use it in the second or third person unless we are referring to it as to have been said by someone, which at that point was also said in the first person by that someone. For example: A asks B, “Nasaan ang libro ko?” (Where’s my book?). B answers with, “Ewan ko”. A is not happy with that answer so A counters with, “Anong ewan mo?”. This use of the second person “mo” came about because A is referring to B’s answer of “Ewan ko”. So A is testily asking, “What do you mean, “you don’t know”?”. Their interchangeability, however, may no longer be possible if something else follows these expressions. For example: "Hindi ko alam ang pangalan niya" (I don't know his/her name) cannot be said as, "Ewan ko ang pangalan niya", to mean the same thing.

Formal: Hindi ko po alam. / Hindi ko alam. Informal: Ewan ko. / Malay ko.

Hindi ko alam.

(continuation) When these expressions are followed by another phrase, think of "ewan ko" as "I don't know about". So, “Ewan ko ang pangalan niya” becomes “I don't know about his/her name.” As is, that won't sound right though. But if that becomes part of a longer sentence, e.g., "My name was already called, but I don't know about his/her name", it will be all right. Consequently, with the "about" in there, you should now use "ewan ko" and not "hindi ko alam" for its Tagalog translation - "Natawag/Tinawag na ang pangalan ko pero ewan ko ang pangalan niya". Quite often, these expressions are used before the word “kung”. “Kung” normally means “if/whether”. When followed by question words – ano (what), sino (who), kailan (when), bakit (why), paano (how), alin (which) – “kung” may be interpreted as “as to”. Hindi ko alam kung ano ang pangalan niya. = I don't know (as to) what is his/her name. Ewan ko kung ano ang pangalan niya. = I don’t know about that which is his/her name. In the last example, “kung ano” was translated to “that which” to allow the “I don’t know about” (ewan ko) to precede it. However, as a rule, either “hindi ko alam” or “ewan ko” may be used if the phrase immediately following it begins with “kung”. Hindi ko alam/Ewan ko kung bakit. = I don’t know as to why. Hindi ko alam/Ewan ko kung alin. = I don’t know as to which one. Hindi ko alam/Ewan ko kung matutuwa ka. = I don’t know if you’ll be happy (about it). Hindi ko alam/Ewan ko kung matutuwa ka o hindi. = I don’t know whether you’ll be happy or not (about it).

They are just the same but "Hindi ko alam" is more formal way to say I don't know. Ewan ko (aywan ko) is the informal way. But there are some circumstances where it is more appropriate to use "Hindi ko alam" than "ewan ko". I just don't know how to explain it. I suggest sir that you use "Hindi ko alam" instead of "ewan ko." :)