How to Solve Bernoulli Differential Equations (Differential Equations 23)

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I’m not even in Diff Eq anymore, just stopping by to say hi lol. Sending good vibes from Florida!

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I agree, but you could write this as a constant lol

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y'all call it calc 4, differential equations

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@@abdallababikir9154 Yeah that's pretty weird. I've heard some schools mix linear algebra with ODE and call it Calc 4. Calc 4 at my school is just Vector Analysis.

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im sorry Calc 4?

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@@warwick802 Calculus 4: Revenge of the Limit

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So I watched this video and the other homogeneous equation video yesterday night and this morning and was able to figure out 3 of my 4 exam problems (open notes). I want to thank you Professor Leonard for your videos because I would definitely have not been able to do my exam without your in depth explanations and tips 🙌🏽❤️

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Please see my Chanel (Abdulhussein Alsultani) to see the differences between my method in solving th e examples) Thank you very much.

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[@jarvisty3640]

This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.

[@rudnam]

I'm so so thankful for this really. My prof introduced diff eqs, its properties, separation of variables, linear DEs and integrating factors, and bernoulli's equation all within a span of 40 minutes and i could barely understand anything. You're a lifesaver

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For this presentation he's wearing a long-sleeved shirt without the sleeves rolled up. Good idea - this is serious subject matter, and we students can't be distracted by those biceps.

[@TalkswithJinesh]

Thank you professor for the video. Looks like there is a typo at 24:05, Ce^(-2x) - 1, but you wrote + 1

[@moussapascalkone7073]

He rectifies it later at 24:54

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Today I did the second example by myself when a few days I had no clue what any of this was including a foggy idea on u-sub. It's crazy how many leaps in knowledge I'm experiencing from just following these videos. Thank you thank you thank you. Can never be overstated how much your help guides people like me who thought they were hopeless. You're the best!

[@mpmndza]

Just a thought for the first problem at (6:24). If v = y^(-2), then dv/dx = -2y^(-3)dy/dx. If you divide the whole equation by y^3 you will be able to substitute in (-1/2)(dv/dx) directly. From there you can put it in linear form and solve. Saves you from all of the fraction exponents. Hard to explain in text but you essentially do two substitutions that gets you to dv/dx +2v= -2 in less steps. That's actually the brilliant thing about using substitution methods.

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[@studywithankitadas]

I scored pretty good marks in maths in my initial semesters because of him... when he had stopped making vedios i had no choice so left maths and took another subject as minor.. my syllabus for this sem was differential equations even though I dont have the subject anymore I still watch his vedios 😁😁

[@jarvisty3640]

This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.

[@daltoncarlson2402]

Yes..., yes you make sense!!!! The hand-waving is yet explained again!!! Thank you, Sir!!! This beats the heck out of a zoom white board where all we get is a non-rigorous proof (because coming from Calc III Students know what that is....not at all), of Bernoulli's DE's, then thrown into examples where the product rule is bypassed when we learned it, LIKE, yesterday. As a student, I do not need five shorthand examples in chicken-scratch on a digital whiteboard over zoom, I need 1 or 2 examples that dive into the details as you do in your videos. You're the Clark Kent of Mathematics, yet be the one who has found the Kryptonite of college paid professors that lack a basic understanding of how to actually teach what they understand themselves!

[@NeverendingAbyss]

Even after I'm done with the diff eq class this semester, I will anxiously wait for the rest of your lecture videos. Hands down the best explanation anyone has given on Bernoulli's.

[@Siawash777]

I am a Mechanical Engineering major at UNF. I find your videos extremely helpful. I do tell everyone to watch your videos when I saw an opening

[@jackpeters2038]

I just spent 6 hours trying to work through this one math problem on homework not including the 4 hours spent the day prior. I looked at videos, notes, re-watched lectures, and asked peers, but I just was not getting anywhere. Finally, after all that stress and pulling my hair, I was able to follow the process, know what I was doing, and FINALLY get the correct answer. I cannot thank you enough. My grades are everything to me right now. Thank you.

[@WilliamMansfield-w3h]

Thank you Prof Leonard! This class has been a lifesaver. Hoping you come back soon and give us a Linear Algebra course! Taking it next quarter and don't know how I'll make it without your help.

[@olivermogga6956]

This is the most effective lecture on Bernoulli Differential Equations I have ever had.

[@jakeb110]

this absolute unit of a man is going to be the reason I pass my differential equation class god bless you good sir

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You have a gift for teaching and explaining complex topics. Thank you for providing these lectures for free to everyone

[@Explorer982]

Long but useful and necessary. I tried learning this with quick 10 min videos but it wasn't cutting it. This is the kind of step by step explanation that works for complex topics.

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[@ILikeWeatherGuy]

"leveraging the derivative of the power rule to undo a power rule inside of a product rule to undo that to find your original equation"= this video.

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this is the only one on youtube that doesnt make you remember the general solution. thank you

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11:35 "that garbage" lmao i love this prof

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[@basilhsxatzhkostas]

Just watched the whole thing and I finally understood Bernoulli!, thank you so much superman!

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[@jarvisty3640]

This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.

[@Juan_Carl0s]

Amazing, you've taught me all Cal classes + some stuff we didn't cover in my Differential Equations class (like in this video). A little comment I have is that I feel that you could've maybe done the work for all n to show how it always simplifies to a linear ODE. Keep up the good work!

[@jarvisty3640]

This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.

[@jc-td4cc]

This helped me immensely. Thank you so much, sir!!

[@abdellatifbourhim8721]

These computations can be simplified. Indeed, set v=y^{-2}, you get that dv/dx=-2y^{-3}dy/dx. Then divide both sides of the equation dy/dx - y =y^3 by y^3. You get y^{-3} dy/dx -y^{-2}=1. So, (-1/2)dv/dx-v=1 or dv/dx+2v=-2 or dv/dx=-2v-2. This is a simple separable equation dv/(-2v-2)=dx. Now integrate both sides: (-1/2)ln(|v+1|)=x+c. This implies that ln(|v+1|)=-2x+C. Finally, apply the exponential and solve for v to get v=-1+Ae^{-2x}.

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Bernoulli is a name appeared very often in Fluid Mechanics.

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[@The1RandomFool]

As an alternative way to derive the substitution, you can divide both sides of the equation by y^n. Then the indicated substitution becomes easier to see.

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This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.

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[@Danny-ql2it]

The first example was also a separable equation, -2 goes to the right side, you factor it out to get -2(1+v). Then just divide by 1+v and integrate

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[@VndNvwYvvSvv]

It's good to practice the theory for linears, but like Bernoulli always gives a result, you can shortcut the linear to y = 1/rho • ∫ rho F(x) dx, or in this case v= and back-substitute. Just be careful to apply 1/rho (or 1/mu) to the entire integral including C.

[@abdhq2299]

I just wanted to mention that at 54:33, where you get the Linear differential equation, it turns out you can also solve it by using seperable equations. You can bring 6xv to the right side and factor 6x out...

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This type of equation randomly showed up during the solution steps for one of the example problems in my Applied Mathematics course about perturbation theory, and I had forgotten about it.

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My friend recommended this channel to me. It is really helping me study for my first DiffEQ exam. I did notice a POSSIBLE ERROR at 24:20 bottom right-hand corner. V=Ce^(-2x) -1 does not = Ce^(-2x) +1 Great video. Please keep making videos! This is crazy helpful!

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[@jarvisty3640]

This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.

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Just learned homogenous and Bernoulli equations a couple hours before my exam today using your videos, and I felt like I actually knew what I was doing on the exam. Thanks for being a great teacher!!

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Two years late, but I also have a diff eq final tomorrow

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@@aaron.glidden3yrs late but I don’t have diff eq final tmro

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[@Mark-di6cz]

Thank you so much for the lectures. Do you think it would be easier to get the equation in standard form, then multiply through by the reciprocal of the y^n on the right side. Then substitute, that way you don't have to solve for y in the v=y term. Just take dv/dx and substitute on the left side dy/dx term.

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THANK YOU

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[@zaga32]

Just a suggestion why not divide everything by y^n then just substitute your v=y^(1-n) and dv/dx = (1-n)y^(-n) * dy/DC. That way you avoid having to do the multiplication and simplifying at the end. Maybe that can help :).

[@ivankaraivanov6152]

Thanks for the video. However, I want to point out that at 8:47 you wrote y^2 = v^-1 => y = v^(-1/2). Correct me if I am wrong, but I think you should have written y = (+,-)v^(-1/2) instead. So I am not sure if you are allowed to make the following substitutions as you did.

[@abdallababikir9154]

the plus minus gets absorbed by C

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awesome work on explaining this

[@jarvisty3640]

This link kzbin.info/www/bejne/poSsooikha6ehpY is also a nice video on Bernoulli's Equation.

[@angelicafoster4488]

Hello is there a Differential Equations book that you would recommend?? Which one do you use when you teach?

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Much love Professor!

[@nagozerafrank158]

sir thanks but which method are you using after obtaining the integrating factor when you are about to reach the step of substituting back V

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[@robertbrandywine]

The thing I can't "see" is why *minus* n? 1-n can be restated as +1-n or -n+1. If we just wanted a difference of 1 we could have used n+1 (or 1+n). Is it because when you differentiate a function of x^n you always get nx^n-1?

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Do you have a video for Euler's Method? Also thank you for all the help. Saved my buns in Calc 3

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You are a freaking champ dude, I wish schools and textbooks taught like this. This was very clear and it helps a lot that you explain the logic behind the method.

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He’s back.

[@ProfessorLeonard]

Yep! I took a break for Thanksgiving and I'm going to take another for Christmas Break, but I will certainly be filming again in the Spring and until this project is complete. Enjoy!

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Professor Leonard You are a living legend. Respect and Love, I have learned a lot from you Sir and still learning and will definitely donate in the near future cox I maybe getting a job :D.

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[@fooliemon]

At about 43minutes, why do you leave the Cx^4, instead of absorbing the x^4 into the C?

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Learning calc through you for electromagnetics. Do you have any idea how many videos this series might have?

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The first equation can be done by variable separation right?

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