Separable First Order Differential Equations - Basic Introduction
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- Опубліковано 8 лют 2025
- This calculus video tutorial explains how to solve first order differential equations using separation of variables. It explains how to integrate the function to find the general solution and how to find the particular solution given the initial condition. This video contains plenty of examples and practice problems.
Integration - Free Formula Sheet: bit.ly/3XCT6oz
Applications of Integration - Free Formula Sheet:
bit.ly/3ZdKSnK
Differential Equations:
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Calculus 1 Final Exam Review:
• Calculus 1 Final Exam ...
Integration - Free Formula Sheet: bit.ly/3XCT6oz
Differential Equations: www.video-tutor.net/differential-equations.html
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The UA-cam 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.
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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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and if you subtract c2 from both sides you also get c ?
@@Concept_3_14subtracting a constant result in a constant same apply in multiplying/dividing etc.
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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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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|.
I got that solution too and was a little confused when he got just 5. Thanks for your comment
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.
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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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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Love the video.Can you explain why both sides of the function need to be placed on the exponent of e .Thanks 😊
Right? I saw a vid where you can only use e as a base if both sides of the function is a natural log🥲
very late reply, bc you need to get rid of the Ln() so you need to use e^
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All remaining equations will BOW TO THE FIRST ORDER!
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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2:30 why there are -1 on both sides thank you
solve for c
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in example #2 I got y=2x+C and it worked
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Please give us more examples... btw, thanks a lot for the vid. It is helping me alot
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1:24 how would that just be considered C? Is that a property? How did he go from 3C to C? Is it because C can be anything? I need an explanation!! Lol
This is super late but pretty much he just combined the 3 c s into 1 constant C. So c + c + c = 3c = ( the new) C
How do you know which side to add the plus C?
Tan(180) and tan(360) also give 0, or every 180 degrees to be precise. So value of c could be 179 and 359 as well.
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