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.

[@omarkazeem3163]

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 👏👌

[@leratomokoena1418]

Brilliant explanation thanks

[@tyronekim3506]

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

[@holyshit922]

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

[@youssefabdedaim2324]

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

[@TanJunYu]

thank you!

[@maharajput1517]

thanks for clearing the point

[@mathwithjanine]

Thanks for watching! :)

[@himanshunautiyal7406]

Thankyou..👍

[@adios04]

thx

[@colinalexandersledge6930]

You are seriously a math tutorial video machine!!!

[@vuwithmeerbabu833]

Thank you plz explain regular and irregular points aswell

[@VishalSharma-cj2yq]

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

[@irisce2799]

i was wondering exactly the same thing

[@VishalSharma-cj2yq]

I think, we usually deal with the positive values of x in ordinary differential equations, that's why she ignored the negative values. (Specially in power series solution we usually solve the problem around a positive ordinary point .)

[@VishalSharma-cj2yq]

But I'm not sure about it, if you find the exact explanation, please don't forget to update me.

[@irisce2799]

​@@VishalSharma-cj2yq I did my hw in my diff eq class yesterday that had similar problems and the right answer was that all values of x that make the argument of the log function

[@VishalSharma-cj2yq]

@@irisce2799 , Thanks a lot for your confirmation.

[@Srishti828]

Thanku you have explained everything perfectly

[@cosuins123forlife]

Thank you this video made me understand singular points!!