How to solve differential equations by substitution

A basic example showing how substitutions can solve differential equations. The method is a very powerful technique.

[jerberus]

Thanks.  Our teacher only gave half-finished problems today in class...in a freaking fast summer course. This helped a lot.

[DrChrisTisdell]

Best of luck with your university studies and thanks!

[NicholasGreenwood]

Exactly what I needed. Thank you for this.

[MultiUU]

When would you use substitution in a differential equation

[SoulBane]

from a student point of view, of course I would choose x+y. it's just intuition, it's the only thing that makes sense.

The part I don't get is how I would use the information you gave me to substitute for a more complicated problem. Perhaps have another demonstration where you have a complicated function where the substitution isn't obvious, and then explain what I'm looking for to make it simpler (what form do I want it to be, what's bad about the current form, are different sub's possible)

[chvits]

will the power substitution will give me always a variable separable equation?

[DrChrisTisdell]

I would use substitution as a last resort (although you could claim that homogeneous equations use a substitution). Good question.

[CrushOfSiel]

Thank you again Dr Tisdell. I don't know how I wasn't following this out of my book. You made it very easy to understand.

[DrChrisTisdell]

It's always a good debate: what is expected to be "recalled"; and what will be given? In examinations we provide a list of integral tables. If an integral isn't on that list then we'd expect it to be "recalled" and / or derived. :-)

[lallouzz]

My university needs profs like you sir... thanks

[jimmykeke]

Some doctors/professors know how to research well, some know how to teach well, but very few know how to Dr C. Tisdell well, such that the once difficult math problems seem to become a lot easier, Cheers for the video

[ixTaKK]

Thanks, I you explained it more clearly than my textbook.

[reubenwilliammpembe]

Thank you Sir - you are the best!!!
#RespectFromSouthAfrica

[treehumpee]

Hey I was stuck on a problem where I have u=y/x. would this derive to du/dx=-(dy/dx)/(x^2) or am I doing it wrong?

[DrChrisTisdell]

Agreed, Perry. I couldn't have said it better myself.

[bryand]

thank you so much, this video is very helpful and concise!

[mariadieguez]

Can someone explain me how to do bernoulli's substitution????

[carstuff]

My prof was switching between notations and it was throwing me off. When i seen you working the problem i think i was more focused on the differences between your methods and less on the problem. We were using prime notation until we substituted back in and then switched to Lebniz. It was my fault

[matthewkarhunglee]

great stuff always come to you instead of my tutors at uni

[SoulBane]

probably the end where you asked "why was this substitution chosen?"