Scales to Play Over D#maj9
Every chord is a subset of several scales: any scale that contains all of a chord's tones fits over it. Pick a chord to see the matching scales from its own root, the major keys the chord belongs to, and full fretboard diagrams for every scale on guitar.
A D#maj9 chord contains the notes D# – F – G – A# – D. Any scale that includes every one of those 5 tones fits over it — from the root D#, that means D# Major, D# Lydian and D# Mixolydian Bebop. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
D#maj9 is also diatonic to 2 major keys: A# major (relative minor Gm), D# major (relative minor Cm). In a song from one of those keys you can also solo with the key's own major scale or its relative minor pentatonic across the whole progression, not just this chord.