From the course: Complete Guide to Differential Equations Foundations for Data Science
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Regular singular points
From the course: Complete Guide to Differential Equations Foundations for Data Science
Regular singular points
- [Narrator] In the previous video, you learned how to solve differential equations near ordinary points. Now let's switch gears and take a look at when you're working with singular points. Let's begin by learning exactly what singular points are. Let's focus on second-order differential equations for this definition. Let's say you have the second-order differential equation, p of x multiplied by y double prime plus q of x multiplied by y prime plus r of x multiplied by y equal to zero. A point is singular at x equals x zero if p of x equals zero and is not analytic. Note though that q of x or r of x must be non-zero at that point in order for this to work. This results in p of x becoming undefined or infinite at that particular point. Let's look at an example of finding a singular point. Sometimes it's obvious such as having x multiplied by y double prime, which in that case, you would often just have x equal zero. But let's look at a case where it's a little bit more complicated…
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