Sometimes, the only difference between success and failure is plain luck. Llewyn Davis (Oscar Isaac), the hapless protagonist of “Inside Llewyn Davis,” is a musician in 1961 New York who wows small crowds at Greenwich Village pubs and bars but can’t catch a big break. His first record, a duo effort he recorded with another singer, flopped, and his partner committed suicide by jumping off a bridge. His second record, this one a solo effort, sold even fewer copies.

Llewyn specializes in traditional folk songs – the movie opens with him performing a sad, soulful rendition of “Hang Me, Oh Hang Me” – but he’s just a little ahead of his time. Popular culture is still transfixed by happy pop songs and 1950s-era ditties, and Llewyn is so destitute he has to resort to sleeping on the couches of friends who cut him a break because they believe in him.

For some quick cash, Llewyn agrees to help out his cheerful friend Jim (Justin Timberlake) on a radio-friendly tune for Columbia Records, but he’s so disdainful of the song he passes on royalties, opting for a small up-front fee.

Jim’s wife Jean (Carey Mulligan) is furious at Llewyn because he got her pregnant during a one-night stand, refuses to take control of his life and is content to drift until the breakthrough he feels he is due arrives.

When she asks him “Do you ever think about the future at all?” he says that’s square and sad. He calls her a “careerist,” the worst thing imaginable to him. He’s an artist and he’s driven by his creative impulses. What is he supposed to do, ignore them and just exist?

“Inside Llewyn Davis” was written and directed by Joel and Ethan Coen, who often take delight in the pain and misery of their characters, especially the arrogant, entitled ones. Yes, the cosmos is aligned against Llewyn: When he spends the night in the empty apartment of some friends, he accidentally lets their orange tabby escape and winds up carrying the animal around with him for days.

But he’s also a bit of a jerk, too: He seems to care more about that cat than he does about people. And when he does try to do the right thing, like visit his ailing father who is institutionalized in a nursing home, his efforts backfire.

Isaac, who did his own singing and guitar playing, keeps Llewyn hidden under a mask of perpetual disappointment and frustration. Only when he’s singing do we get a peek at the real man inside (here’s a rare breed of movie where the musical numbers are transfixing, regardless of your personal tastes, because they’re so revealing of the character’s state of mind – a profound sadness).

Llewyn keeps banging up against failure, long past the point at which most people would have given up, and the world seems to be telling him to wise up (“What are you doing?” reads some graffitti scrawled in a bathroom stall).

But there’s always another chance looming – another possibility to keep hope alive. “Inside Llewyn Davis” is fairly light on plot: Llewyn hitches a ride to Chicago with a pompous, heroin-addict jazz musician named Roland (John Goodman) to audition for a powerful club manager (F. Murray Abraham) who could give his career a big boost.

On the way there, Roland mocks Llewyn for his choice of music and simmers in self-pity. “Why is nothing going right for me?” Roland asks. “Why is my life a big bowl of (expletive)?”

That’s a question a lot of characters in the Coens’ movies could ask themselves (Barton Fink, for one, immediately comes to mind). But Llewyn’s situation is particularly dire, and the merciless Coens allow him no escape. And yet there’s something strangely sympathetic, even admirable, about Llewyn’s refusal to give up.

The Coens refrain from telling you what you’re supposed to think of his music: They’re not even willing to cut him that much slack. But Isaac’s remarkable performance leaves no doubt about the man’s talent.

“Inside Llewyn Davis,” shot with a beautifully diffused color palette by cinematographer Bruno Delbonnel, has a melancholy feel – there’s a lovely shot of red brake lights through a rainy windshield that conveys a great, wistful sadness, a literal vision of Llewyn’s deep depression – and the movie lacks the comic cynicism of “A Serious Man” or “Burn After Reading.”

You may not like Llewyn much, but you don’t laugh at him, either. The Coens take care of that for you, ending the movie with a bitter twist that suggests that along with luck, Llewyn could have benefitted from a little better timing, too. “Inside Llewyn Davis” is one of the Coens’ smallest movies – this one doesn’t have the broad appeal of “True Grit” or “No Country For Old Men” – but like Llewyn’s music, it comes from the heart and is deeply felt. It is also one of their best.