I do wish they'd mention the music and inspiration in the credits. S1E17 (Calypso) is built around Camille Saint-Saens' "Organ Symphony" 4th movement. S1E1 (The Magic Xylophone) is based on Mozart's "Rondo Alla Turca". S1E11 (Bike) is derived from Beethoven's Symphony no. 9 4th movement (a.k.a. Ode to Joy). And the original music is awesome.

Sleepytime uses music from Holst’s “The planets”. In particular the piece called “Jupiter”.

Just Google “holst Jupiter”.

Yeah, I eventually figured that one out - I was actually familiar with the Holst but couldn't place it, so for a while I was just thinking "oh, I know this from somewhere"

Something something national geographic

Though I agree that the songs should be listed in the credits, iOS has Shazam built-in now that Apple bought it, which will recognize songs ("hey Siri, what's this song?"). I'd be shocked if Android didn't have something similar.

I’m not sure if that works since at least for the classical music, they seem to be recording their own versions.

Ah, classical; got it. I frankly have not tried it with classical, but do vaguely recall that others have reported the same. Apologies for the wild goose chase.

It does not work. I've tried.

Most of the music in Sleepytime is Gustav Holst's Jupiter, though I'm not sure right off the top of my head whether that is used for the credits.