Picard–Lindelöf theorem in real world applications

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Okay guys, so my question is easy. Is there any applications of the Picard–Lindelöf theorem in physics or other real world applications? I'm asking because I see that I have a whole course ahead about existence and uniqueness of solutions of differential equations, so I need an extra motivation to study it. My first assumption is that if a differential equation pops out in some model of the world, it should have a unique solution, and the theorem would be useless for physicist. But I hope things are more interesting and strange. I don't know, in quantum mechanics maybe?