How to identify singular points in differential equations | Math with Janine

In this video tutorial, I demonstrate how to identify singular points in differential equations.

This is useful for when we are solving second order linear differential equations of variable coefficients, which have the form y'' + P(x)y' + Q(x)y=0.

A point xo is an ordinary point if P(x) and Q(x) are analytic at xo. Otherwise, it is a singular point. Analytic means that a function has a power series representation at a given point.

[omarkazeem]

WOW 😱 this has been giving me headache for over some hours now I couldn't get a clear explanation untill I came across this video.
Your explanation is superb 👏👌

[colinalexandersledge]

You are seriously a math tutorial video machine!!!

[vuwithmeerbabu]

Thank you plz explain regular and irregular points aswell

[holyshit]

y''+exp(x)y'+5y=0
We can use change of independent variable here
( t = exp(x))
Singular point should appear after this substitution but it will be easier to solve it with power series

[VishalSharma-cjyq]

Awesome explanation, but I have a question in your second example you said that log(x) is not defined at x=0 so, it's a singular point (which is absolutely correct), but my question is that log(x) is also not defined for x<0 so, shouldn't we say all those points where x<0 are also singular points of this differential equation.

[tyronekim]

That was a great explanation on the last example. Nice.

[Srishti]

Thanku you have explained everything perfectly

[youssefabdedaim]

how we can determine a singular point from other singulars point ?

[cosuinsforlife]

Thank you this video made me understand singular points!!