Ciro Santilli
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Applications of Lie groups to differential equations | 🗖 nosplit | ↑ parent "Lie group" | 96

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Solving differential equations was apparently Lie's original motivation for developing Lie groups. It is therefore likely one of the most understandable ways to approach it.
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It appears that Lie's goal was to understand when can a differential equation have an explicitly written solution, much like Galois theory had done for algebraic equations. Both approaches use symmetry as the key tool.
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