Classifying Singular Points: Regular or Irregular?

In summary, a singular point is a point on a graph or function where the derivative is undefined or infinite. It is important to find all singular points as it helps us understand the behavior of a function and identify critical points. To find singular points, one can take the derivative of the function and set it equal to zero. A function can have more than one singular point, which occurs when the derivative is undefined or infinite at multiple x-values. A critical point is a point where the derivative is equal to zero, while a singular point is a point where the derivative is undefined or infinite. Not all critical points are singular points, but all singular points are critical points.
  • #1
Success
75
0

Homework Statement


Find all singular points of xy"+(1-x)y'+xy=0 and determine whether each one is regular or irregular.


Homework Equations


The answer is x=0, regular.


The Attempt at a Solution


I know that x=0 since you set whatever is in front of y" to 0 and you solve for x, right?
And I think you supposed to take the limit as x approaches to 0 but I don't know which function to take the limit of.
 
Physics news on Phys.org
  • #2
Have you looked in your text to see the definition of a regular singular point? What is it?
 

Related to Classifying Singular Points: Regular or Irregular?

What is the definition of a singular point?

A singular point is a point on a graph or function where the derivative is undefined or infinite, causing the graph to have a sharp point or corner.

Why is it important to find all singular points?

Finding all singular points can help us understand the behavior of a function or graph at certain points, and can also help identify critical points that may affect the overall shape of the graph.

How do you find singular points?

To find singular points, you can take the derivative of the function and set it equal to zero. Then, solve for the x-values that make the derivative undefined or infinite. These x-values are the potential singular points.

Can a function have more than one singular point?

Yes, a function can have multiple singular points. This happens when the derivative is undefined or infinite at multiple x-values.

What is the difference between a singular point and a critical point?

A critical point is a point where the derivative is equal to zero, while a singular point is a point where the derivative is undefined or infinite. Not all critical points are singular points, but all singular points are critical points.

Similar threads

What Determines Regular and Irregular Singular Points in Differential Equations?
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Identifying Types of Singularity in Differential Equations
    • Calculus and Beyond Homework Help
Replies
6
Views
2K
Finding regular singular point
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Singularities when applying Stokes' theorem
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Find the dimensions that will minimize the surface area of a Rectangle
    • Calculus and Beyond Homework Help
Replies
1
Views
600
How to calculate a sink using spherical coordinates
    • Calculus and Beyond Homework Help
Replies
7
Views
797
Verify Green's Formula for a Simple DE
    • Calculus and Beyond Homework Help
Replies
1
Views
616
Find limit of multi variable function
    • Calculus and Beyond Homework Help
Replies
10
Views
957
Stationary points classification using definiteness of the Lagrangian
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Solve p = P(2X <= Y^2) using double integral
    • Calculus and Beyond Homework Help
Replies
4
Views
973

Hot Threads

Recent Insights

Back
Top