Separable Equations with Initial Values (Differential Equations 13)

[@spcverger]

Prof. Leonard is a life saver. I'm three weeks in to Diff EQ at my Community College, and I was completely lost. Professor was not explaining anything, just reading powerpoint. Much to my joy, I found out Prof. Leonard was also doing Diff EQ (he saved me in Calc already). Just two days of watching these videos, I'm totally getting it. You, sir, are a fantastic teacher, which is the highest of compliments. Thank you, thank you, thank you.

[@ProfessorLeonard]

I'm very glad to be of help and am certainly glad the videos are making this tough subject understandable to you. Good luck with the rest of your course!!

[@1willFALL]

You inspire me to study more upper mathematics (PDEs, Numerical Methods, Complex Analysis) and get buff. Thank you.

[@bonjourcanada4639]

Exactly.

[@zaynbashtash]

This human being makes me regain faith in humanity. Thank you professor.

[@zatch5166]

My favorite jacked professor. Thanks, you've helped improve my grade dramatically! Thank you so much!

[@stephanm.tjaden3887]

Professor Leonard, your videos are so awesome it is ridiculous! I love it and cannot thank you enough for helping me master Trigonometric integrals. They were almost the end of me. Keep doing what you do and never stop!

[@NeverendingAbyss]

Thank you, professor Goku

[@michaeldavis5815]

I like how he understands that other professors suck at teaching. He actually takes the time to thoroughly explain each step, and not just skip around.

[@W_Ivar]

One of my students has trouble with this subject (I still do too), so Ill share the vid with him. Thx! Simple and clear 👌🏻

[@LifttheDead30]

So, "write absolute value of y equals all this garbage" lol. Love this guy so much. All subjects he teaches are easier to understand than any math lecture I have ever attended in University.... by FAR.

[@brittneypugh2480]

I love these video lectures! They are so easy to follow!

[@nicholasf.75]

Professor Leonard, your explanations are immaculate. Thank you for putting out such useful content. May our Lord and Saviour Jesus Christ Bless you my Sir.

[@mohamedramadanmohamed3744]

Really you make everything clear,I like that.THANKS PROF. LEONARD

[@Shene-z1y]

thanks alot best professor in the world ever

[@Ncandeyans]

Juiced up and better than ever, lookin saucy my guy

[@krshivamraj5755]

you are professor or a bodybuilder.....my god!! just look at those biceps😱😱😱😱

[@rockyshepheard6054]

Can someone tell me how in min 20:14 Prof Leonard added to 'just one side...but not to the other. That seems highly incorrect. Thx

[@tanvirtscientist608]

you are my real life superman sir!

[@Rick_Sanchez_Jr.]

We just started learning this today in our Calc 2 class. This video helps a lot, thank you

[@carlsssoon]

Your board rubber is so freaking good, it is so satisfying

[@iWantToBecomeTea]

Hi! Quick question: on 15:23. Why we can drop the absoulte value? I know that after it is no longer inside the ln we don't care about the sign, but still it was in ln, meaning that we need to adopt the x variable, right? (Of course I understand why we can do that with |y|) Thank you in advance!

[@oximas-oe9vf]

at 15:50 why do we remove the absolute value sign from the sin(x) function?

[@IMadeOfClay]

At 33:07 why is square root 4 calculated as +2 rather than +/-2? Why did you take the positive square root? And thank you sir for your videos.

[@dedstrock]

MadeOf Clay Because otherwise C1 would have been equal to -3.

[@IMadeOfClay]

Thanks for replying. But what's wrong with C1 being 3 instead of -1? Or are they both valid solutions?

[@natepolidoro4565]

Yeah, c1=-1 & 3 also

[@pizzawhisker]

Late to the party but problem is if you try c1=3 then the initial value doesn't work. Sqrt4 is never -2 btw

[@RahulSharma-qi6mb]

You inspired me to get buff

[@yasseralharbi3317]

Welcome back doctor

[@RahulSharma-qi6mb]

The Goat of mathematics

[@iExplorer64]

you saved my life

[@chemicalengineeringbd7614]

Thank you professor. May allah bless your life and give you happiness.

[@astrageekette9692]

You cost me a client! I'd helped a friend's kid with math some years ago and now that she's in college, she asked if I could give her some pointers with DiffEQ. Came across your videos and told her to take a look before we got together. Well, she called to say thanks for sending her to Professor Leonard. How 'bout a finders fee? LOL

[@astrageekette9692]

"It is obvious that she no longer needs to see me."

[@azharmahmood974]

very good sir from pakistan

[@Sim-TruckingonaBudget]

YOU ARE THE BEST!!!!!

[@berk1179]

Love the Darth Vader on the background

[@yhe7590]

Could you do extensive Integration?

[@mathewmiller730]

@Professor Leonard, for the first example is the answer ln|y|+e^x + ln|2| correct doing it the way where you plug in the value earlier? Thanks.

[@mathewmiller730]

In his first example is the answer ln|y|+e^x + ln|2| correct doing it the way where you plug in the value earlier?

[@shubhammodanwal6713]

quality material..🙏🙏👍👍

[@taekwondotime]

@26:45 *Possible error:* When you separate the exponents that are being subtracted, don't you have to write those as a quotient? e^(2x-y) should be e^2x / e^y

[@zsoltbalazs7551]

it's the same dividing by e^y is the same as multiplying by 1/e^y (which is the same as e^-y)

[@aryannallanez7894]

What integral tables are you using that work so effectively? I have been looking online, but anyway you can provide a pdf?

[@andrewmuleme6125]

where is the C1 that you are putting on top coming from and what does it mean? anyone to help me with an answer

[@khhassan9810]

In the last ex .. is the root of 4 is positive and negative 2 ? so why we chosen negative and did not choose positive ? ......

[@scorpionedge]

is Y = tan(x^3 + 1) a wrong answer? (solving for C = 1)

[@bunstie5208]

hey for question 2 imagine there was no 3x^2 and instead just y^2 +1... would this still be possible? youd just divide y^2 + 1 from both sides and integrate the left and right even tho the right would only be dx

[@iamstokk]

Post some lifting videos my guy

[@liampereira6031]

Hello Prof. Leonard! quick question would it be correct if I got the following solution? y=pi/2(sqrt((sinx)^2)) the reason for this is so I could lose the absolute value sign, the difference I am spotting is that the way I have it, my solution will never be equal to a negative value. Thank you in advance!

[@JoshuaWorleyWindle]

Differential Equations is broken into two parts at the University I'm attending. Do these videos cover both Diff Eq 1 and 2 or just 1?

[@pagmanproductions1686]

the chad of math

[@javieracosta8578]

What is the integral of those biceps?

[@Peter_1986]

That integral would approach infinity.

[@drewpass5697]

For the 2nd problem where the solution is y = tan(x^3 + pi/4), wouldn't 5pi/4 also work for C. And by this logic, 9pi/4 works along with 13pi/4. So, would it be too much to say C = (4n+1)pi/4 where n is any integer? Am I over complicating than what it needs to be? Or does it specifically need to be pi/4. Your videos have been awesome by the way! Great at breaking things down

[@Syndicalism]

I know this is beyond late the output of arctan(y) is only between -pi/2 and pi/2 and as such, pi/4 is within that output while 5pi/4 is not. In the limit as the input, y, approaches infinity of arctan(y), the output approaches pi/2 which means the output without any limit taken will always output some number thay is infinitely just below pi/2 which is ~1.57. The output is defined for {x|x =/= [pi/2 + (pi * n)]; 5pi/4 (which is [pi/2 + pi * (3/4)]) is ~3.93, which is > 1.57 and therefore does not exist. So yes it specifically has to be pi/4 because there is no input y, that results in tan(y) = 1 and can simultaneously be plugged into arctan(y) such that the output, x is less than (+or -) [ pi/4]

[@əliabdulkərimova]

Maybe God be pleased with you,Amen🤲

[@noahd8673]

on the first example he should waiting to the end to solve for C and solving for C in the middle, and should that you got the same answer, but he got that C=2 and c1=2, but if u substitute c1 as two into the most simplified equation for with y, you would get y=+ -2e^e(e^x). if you tried to see verify this, you would see that you can only get the positive option, but where was the mistake that led to the negative in the first place?

[@tanvirtscientist608]

thank you sir!

[@abdulrazzaq9726]

Add more videos lecturers for graduate and post graduate classes.

[@ElifArslan-l9g]

thank you

[@edwindeebs4524]

Doesn’t Ln=ln just cancel instead of you using “e”. I thought they just canceled by the logarithm rule

[@natepolidoro4565]

ABSOLUTE VALUE OF SINE 15:38

[@theoendre6484]

He didn't write them because they were replaced by the positive & negative signs.

[@stevenstratvert6664]

Any recommendations as far as a textbook?

[@robertbrandywine]

For differential equations? Differential Equations by Stroud and Booth. You can find it on Ebay.

[@stevenstratvert6664]

@@robertbrandywine Hey Robert..yeah I meant to say Differential Equations. Thanks!

[@zac1893]

Watch this on 2x speed and he’s a genius steroid meth monster

[@kvnagendra5354]

I've seen 30 sec of kitkat ad completely

[@berthamumba7200]

When are you starting homogeneous of differential equations? 😊

[@Peter_1986]

He has several Homogeneous videos further down in the playlist right now.

[@gamesandmods2042]

Hi.... Sir can i ask you? best book for hyperbolic functions. i want to practice with examples. i need to preparation but i don't know from waht book do i prepare plz suggest me the book name anyone else tell me the name of book? sorry for my bad engish.....

[@jamesgu1755]

Calculus 7th by James Stewart

[@gamesandmods2042]

Thanks Sir

[@doggiegirls]

I LOVE YOU

[@adkm222]

thanx

[@chukwuebukaekenedili224]

Someone can be not an amazing singer but work on it and make good music.

[@dongiovanni8899]

Wear singlet

[@pabloescobar4029]

MVP

[@Euphemia-em8fe]

Done

[@khbye2411]

e^ln(mod(X)) ...does it simplify to just X or the mod of X (absolute value of X)?

[@robertbrandywine]

What is mod here?

[@khbye2411]

Absolute value

[@khbye2411]

Around 22:30 in the video

[@khbye2411]

OK I get it now! The 16th video he pinned a comment and in 17th video he also talked about it--the domain of x. In this case, I think he assumed the domain to be x>0. So there's no need for the absolute value signs.

[@muyuanliu3175]

wrong answer in case = 2x^2y due to dual absolute symbol

[@gamesandmods2042]

sir plz tell me

[@JonLG490]

this shit litty