Separable First Order Differential Equations - Basic Introduction

[@TheOrganicChemistryTutor]

Integration - Free Formula Sheet: bit.ly/3XCT6oz Final Exams and Video Playlists: www.video-tutor.net/ Calculus 1 Final Exam Review: kzbin.info/www/bejne/jZ6lq6B-p9pqbtk Next Video: kzbin.info/www/bejne/oaiqpp6PlJekjbM

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Time to study for my Differential Equations final in 11 hours. Wish me luck

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How did it go? :O

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Chandler Janssen i wouldn’t be surprised, Finals are Hell no matter what subject, and Differential Equations is also Hell, therefore Differential Equations Finals = Hell^2

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[@postholedigger8726]

The KZbin learning format is exponentially better than any other university learning format. It offers the opportunity to actually UNDERSTAND instead of MEMORIZING the material. With a few mouse clicks A lecture can be repeated until the problem is understood. It can also be paused to gain any necessary background information required to understand each step. Working out the reason for each step can take time, from minutes to days, which would not be possible in a traditional classroom. Not only is the educational format better, but many more students can be reached. This particular video, as of 2/1/2017, has 834,351 views. As of now, 3/15/2022, the number of views has to be in the millions. No college professor in any traditional classroom format can come close to lecturing the number of students represented in those views. david

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[@shotono3286]

At 1:00, he only adds C to the right side because when you integrate, on the left side there's a c1 and on the right there's a c2. When you subtract c1 from both sides, you get a c on the right side that isn't c1 or c2. I hope this helps, because I was wondering why he did that myself.

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[@Concept_3_14]

and if you subtract c2 from both sides you also get c ?

[@0danP]

​@@Concept_3_14subtracting a constant result in a constant same apply in multiplying/dividing etc.

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hey folks, we made it to differential equations with this guy!

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[@karlbjorn1831]

At 4:04 you can't just ignore that its ln |y| and not just ln y. When you substitute e^c for C your new constant C wouldn't include negative numbers since e^c never is negative. BUT if you used |y| it would simplify to ±e^c which includes negative numbers.

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10:09 where’d you get tan(0) from???

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All remaining equations will BOW TO THE FIRST ORDER!

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[@kj1857]

At the solution completed at 6:43 , is it only me who noticed that e^c is not simply c. e^ln c is C but not e^c. c is suppose to be ln |5|.

[@grasshopperweb]

I got that solution too and was a little confused when he got just 5. Thanks for your comment

[@cbookins]

No. C is simply a number like 5, 21, 100, etc. and e is also just a number 2.72. 2.72 raised to any number is still just going to be a constant, so it is just c.

[@vez3834]

Because e^(ln 5) = 5... it doesn't matter whether you put 5 or e^(ln 5). Thus, we can just mark e^c as c. Another way to think about it is that e is a constant and c is a constant. Constant to the power of a constant is itself a constant. So e^c can be rewritten as just c. The point of c is not to keep the exact form of whatever you did, but to make make the integration happy. Making it a simpler number makes for easier calculations later.

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[@sammyabo-abo6652]

2:30 why there are -1 on both sides thank you

[@HESOYaM097]

solve for c

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please do more diff E videos !!

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How do you know which side to add the plus C?

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[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for an excellent Introduction to Separable First Order Differential Equations. This is a simple topic that all students should understand in Introductory Differential Equations. At the 4:37minute mark, there is an absolute value sign missing after the ln. This occurs in the final example in the video. Please correct this small error in the video.

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Thank you so much. The textbook I've got for my class sucks. It literally gives examples for its explanation but leaves them half solved or just before the answer to go on to explain another concept. I can actually understand you and not play riddle games.

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Yeah i have an exam in 2 days, and i am studying this topic rn. It will mostly be on this topic. I hope i get an 80 or above on it.

[@Graylonerem]

6:00 what makes e^C=C ... is it a rule ??

[@theodoresweger4948]

Very good I had forgotten and this is where I left off . Well explained thank you.

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I’m watching this in my differential equations class right now

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the best lecturer

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[@tommyjoseph8630]

Love the video.Can you explain why both sides of the function need to be placed on the exponent of e .Thanks 😊

[@jansmith7387]

Right? I saw a vid where you can only use e as a base if both sides of the function is a natural log🥲

[@Iamme0101]

very late reply, bc you need to get rid of the Ln() so you need to use e^

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Thanks for clearing my confusion

[@dusea10]

0:57 When you antiderive y squared, would you not have a different constant, C? Sorry, a little confused.

[@PSIPlays]

Technically yes, and no. Let's say you left the answer as C/3 for example, and kept solving, you would get a "different" C value. This is true. However, if you solve the problem for any x value for a certain y value, C will always compute the same one. For example, if the "normal" C he had in the video was 60, your C/3 would compute (for C) to 180. The answers would be equivalent. Try them out :)

[@ahmedsarker3555]

3:53 why do we write 1/y instead of integration of dy or 1dy

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[@belacile]

4:00 Why did you get rid of the absolute value? Doesn't that effect the rest of the problem??

[@Alaaalshoaiby66]

Can you do exact and non exact differential equations pleaeaase?

[@god_account-2437]

why is it that the factor in front of the constant not affecting the constant, 3c=c??? how

[@Youngballer739]

Because C is some unknown constant, so it does not matter by which factor it is being multiplied, it is still just an unknown constant.

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[@ahmetenesacar2326]

The last question has 2 answers depending on where you put c

[@beshoyasaad3427]

in example #2 I got y=2x+C and it worked

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Also in 2:40 why is it that 8 = 1 + c is being subtracted by 1s? Why?

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great video sir 👍🏾🙏🏾 Thank you

[@manloloyojosh1458]

Can someone tell me why there is a + c in 1:00 ? Where did the c come from?

[@ScilexGuitar]

The c comes from integrating. Think about it from the other way. When you differentiate a constant, what do you get? Nothing right? So when we integrate, we dont really know if there is gonna be a constant or not. The c might be anything, it might be 0 aswell. Thats why you need an initial condition to figure out the particular solution, i.e. the value of c

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I feel like everyone can have a different solution and a different idea of solving that by the way he simplifying it

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You got this bro keep trying