= Applications of Lie groups to differential equations
{tag=Analytical method to solve a partial differential equation}
= How to use Lie Groups to solve differential equations
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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.
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.
* https://www.researchgate.net/profile/Michael_Frewer/publication/269465435_Lie-Groups_as_a_Tool_for_Solving_Differential_Equations/links/548cbf250cf214269f20e267/Lie-Groups-as-a-Tool-for-Solving-Differential-Equations.pdf Lie-Groups as a Tool for Solving Differential Equations by Michael Frewer. Slides with good examples.
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