Questions & Answers about Twój problem jest podobny do mojego.
Why is mojego in the genitive case here?
The adjective podobny (similar) is used with the preposition do, which forces the following word into the genitive case. Because of this rule, "similar to mine" translates as podobny do mojego.
Where is the word for "problem" after mojego?
Just like the word "mine" in English, you do not need to repeat the noun in Polish. The possessive word mojego stands perfectly well on its own, though it keeps the masculine gender of the implied noun problem.
Could I just say podobny do mnie?
If you said podobny do mnie, it would mean "Your problem is similar to me," comparing an abstract issue directly to you as a person. To compare one problem to another, you must use the possessive pronoun mojego.
Why does podobny end in -y but mojego ends in -ego?
Podobny describes the subject of the sentence, Twój problem, which is in the nominative (basic) case and takes the standard masculine adjective ending. However, mojego comes after the preposition do, which changes its case to genitive and gives it the -ego ending.