Solving Differential Equations with a Composition (Obvious) Substitution (Differential Equations 22)

How to solve Differential Equations with a on obvious substitution that typically involves a composition of functions.

[buddhakonwar]

If someday in future I achieve something in mathematics then I'll give all the credit to you for making my base strong enough to deal any kind of mathematical problem. Thank you so much Sir.

[husamobaid]

I can't thank you enough. Your efforts are changing people's lives for the better.

[scorpionedge]

Best prof on the planet! Never stop this incredible talent of yours!

[Frostasy]

I've learnt so much from you over the years. You're helping me so much in my EE program.

[GaryTugan]

Hi Prof Leonard! I found your vids a few months back. They've been extremely helpful in reminding me of specific problem types and their solutions since its been a LONG time since I got my engineering degree from VA Tech (1987). Yeah, so it's been awhile, and since I am now working with students in math and engineering and the like, I like to keep myself fresh in the know. So, thanks for these vids!! In watching this particular vid, I found an interesting point in the 2 different ways you went about solving the integral. At 22:35, you've just shown the u-sub method. And then you go into the other really cool way. In doing both methods, I noticed a difference in the two answers... U-sub gives "v+1- ln(v+1) = x + C", but the 2nd method you showed gets the same thing, but without the +1 part on the left hand side. I realize you can bring the 1 you get when using the u-sub method over to the other side to join the constant and it simply makes a new constant. But still I am most intrigued as to why the two different methods give seemingly "different answers". I imagine you noticed this as well?

[lacelulaqueimplota]

I swear to God I will pay you back the day I am able to. Unfortunately, right now I am a poor bastard. I cannot thank you enough Professor Leonard. Thanks for everything man. :')

[darkcry]

your making the world a better place sir, thanks for yours videos

[geethapillai]

Never knew it was possible to understand calculus to this extent, thank you so much Prof Leonard ^^

[aaronguerrero]

So this is like "Reduction to Seperable"... AWESOME!

[AmitKumar-oqqu]

I will meet you one day just to say you "THANK YOU SIR"

[alrayyaniQtr]

I've noticed you've been stressing yourself over this course. Dont burden yourself with a big promise such as a complete course on DE. The load will be stressful and you'll hate cause it will feel like a job. Just make a video on a topic when you feel like it. You'll find yourself actually enjoying it not stressing it.

[supernovae]

Will you upload solving homogeneous and non-homogeneous differential equations using power series technique? Also the Laplace transform ?

[volkanulker]

can we use trig sub for 33:00 ? We can rewrite equation as 1/ v ^(1/4)^2 + 1^2 and gets arctan

[CHRISTIANZEGARRA]

Question: How far are you in the course of differential equations? Up to this video is this considered half way through the course or beginning? I’m taking differential equations next semester.

Couldn’t have passed calculus 1-3 without your videos.

[mesutbakhtyari]

Definitely you gonna helps me a lot next semester

[BoyleFrancis]

Going to the fitness center worked out...thousands of more subscribers.

[garethpienaar]

24:47 When I use the u sub method for that integral, I end up with the whole integral equating to (v+1 - ln(v+1). And this is different to the (v-ln(v+1)), which is what Professor Leonard got. Which one of these answers is actually correct, because when I google it, I keep getting different answers.

[mausplunder]

really nice video... i think u can drop the abs value on the last answer because sqrt(v)+1 can never be less than zero.

[theoendre]

the substitution in the last example is better to be v^2= x+y+1, it will make the integral a lot easier, you just need to be careful when taking the derivative of v^2 after solving for y, also be careful at the last step when you want to replace the v's, because your sub was v^2 & not v. Hope this will help

[b]

I like it !!! Take it to the other level !!!!💪🏽💪🏽💪🏽💪🏽