Reducible Second Order Differential Equations, Missing X (Differential Equations 27)

[@ProfessorLeonard]

As far as the mistake on the video (example 1): Here is the worked out solution from the point of the Mistake 1/c arctan(y/c) = x + d -- I'm using 'c' for 'c sub 2' and 'd' for 'c sub 3" Multiply by 'c' ----- arctan(y/c) = cx + cd Tangent on both sides ----- y/c = tan( cx + cd) Multiply by 'c' ---- y = ctan( cx + cd) Note!!! 'cd' is STILL a constant ---- call it 'B' and call the constant 'c' "A" So we have ---- y = Atan(Ax + B) Hope this helps!!

[@KimHoang-ee8iz]

Thank you so much for all your works!

[@fahimahmed3490]

this is the topic of my next semester.😍😍 a lots of love and pray for you from Bangladesh

[@mxlexrd]

In order to integrate to arctan, aren't you assume that c1 is positive? If so, don't we need to consider a case where c1 is negative?

[@krishnachaichaiporn1161]

Is it convenient to check before posting? Anyway your videos are great.

[@lesliezhang9203]

Is it y = (A^1/2)*tan(Ax + B) for the final, since 1/(y^2 + C) = 1/C * (1/ ((y/c^0.5)^2 +1). Integral this equation, we have 1/c arctan (y/c^0.5).

[@oshainross5536]

It had been a long wait since the last video, but it's great to have you back, Professor. I'm doing Diff Eq this semester, so I'm always anticipating new content from you. I hope you'll be through by the end of this semester. Oh... and I hope your newborn is still doing well.

[@geethapillai4701]

Your kind words at the end of the video really made my day. Thank you for making mathematics so easy to understand. You're really one of the best lecturers I've ever had.

[@NWAGWUSARAH]

Woow, I have watching your video that was 7 years ago. Good to see you sir, still looking great. Your videos are grade savers 👌🏾.

[@ILikeWeatherGuy]

professor is a gift to humanity :P

[@suryakantadash7441]

Never seen such a dedicated teacher . Thanks professor

[@carlosordonez3352]

Calc 1, Calc 2, Calc 3, Diffe E Q thanks for the help, truly grateful.

[@cruelsummer3021]

thank you for getting me through calc1-3 and now DE, professor! sending you all my support

[@andyrockism]

He used to be a Math Professor at my college.

[@MathTutorVideos]

Lucky bastard.

[@doggiegirls]

used to be? what happened?

[@MrSkrifle]

@@doggiegirls Obviously changed schools??

[@doggiegirls]

@@MrSkrifle how is that obvious dude? I heard some professors got fired for making videos during lectures so I was worried that happened

[@MrSkrifle]

@@doggiegirls he records on his own time, not his lectures

[@KindaAmazing667]

Oh boy! Can't wait to be back here in the fall for Diff Eq. You're already carrying me through Calc II. If every professor taught like you, maybe the half of my class that dropped would still be in the class.

[@londekazama7085]

M watching from South Africa ,Just want to say I appreciate your work a lot and keep it up.

[@oscarobioha595]

thanks mann....been watching ur videos for 3 years now

[@PedroHenrique-es8rv]

I'm still doing calculus 1 stuff. I can't wait to learn about Differential Equations!

[@ILikeWeatherGuy]

21:51- forgot to use chainrule in the arctan, Fixes it in description. Although we should easily see it if we watched his Calc videos.

[@Lestibournes]

also if you think about it, you're multiplying dP/dx by dy/dy, which is multiplying by 1. Then you just rearrange the numerators and denominators to get dP/dy times dy/dx. So, you have: dy/dx=P Divide both sides by dx: dy/dxdx = dP/dx Multiply the right-hand side by 1, in the form of dy/dy: y" = dP/dx * dy/dy Rearrange the fraction on the right-hand side: y" = dP/dy * dy/dx Since dy/dx = P, substitute it for P: y" = dP/dy * P Or: y" = P * dP/dy

[@Robisawolf]

alternate form for the 2nd to last solution is sin(2x)A +cos(2x)B. you may see that in text books elsewhere namely y" +ny'=0 -> sin(sqr(n)x)A+cos(sqr(n)x)B or Asin(sqr(n)x+B)

[@mikem9270]

It's really nice to see you again Superman :)

[@Jcagan87]

Can you make a video on solving second order non-homogeneous equations? You're great at explaining the thought process of what's going on and this video would really help!

[@Teslacoil33]

Phew so lucky I delayed one of my Maths units. Last year this video wouldn't have been out to help me and I'd be screwed! Once I finish my exam I'll be donating to your Patreon Prof!

[@dorelpanciuc6649]

you have the talent to teach

[@imanwafa500]

Good to see you back Profesör

[@orangetree2104]

Thank you for making all this content available for the masses !

[@cmccu010]

Hey Professor Leonard, I just wanted to say thank you for this channel it has given me the tools to get through the first part of ODE! Just wondering if you have any videos in the pipeline for dealing with higher order DEs other then the reduction of order methods. Thanks again!

[@catculus1]

thank u prof, saved my life

[@siddharthtyagi3940]

really sir your way of teaching is great. love frm INDIA

[@nikolozperadze4887]

Excellent job explaining! Love the examples

[@isobar5857]

Great to see you back sir.

[@tangsoopap]

It seems to me in example one you assumed C1>0. If C1=0 then integral is -1/y, if C10), difference of two squares so use partial fractions and integral has logs instead of inverse trig.

[@ruchikathayil2627]

Love your lectures Sir!

[@punyapratyushasethi6048]

The hero we deserve

[@zhaomingsoh4447]

The supposedly correct answer for y''+4*y=0 is y=sin(2xA+2B)*A. I think he missed factoring in the u'=1/sqrt(C3)

[@ebermaciel4336]

You are the real boss man, thank you very much

[@fernandesdylan]

Your a legend...thank you so much.

[@bloodyadaku]

@19:10 What would happen if your C1 was negative? Then you'd get an integral of 1/(y^2-C1) which would be a completely different solution?

[@chrisorr9029]

You are absolutely correct. If c1 is negative one uses partial fraction decomposition instead. The answer you would get vs the one he gets, while they will look different, are actually equivalent. If his c1 is negative, then you get y=sqrt(-c1) * (e^r + 1)/(e^r -1) where r is 2(x+c4)sqrt(-c1) (where c4 is just another constant). The reason this solution is the same as his in disguise, is that tan x = -i * (e^(ix) - e^(-ix))/(e^(ix) + e^(-ix)). They're the same, but what he probably should have pointed out is that if his c1 is negative then those constants he's throwing around are not necessarily real (in fact at least one of them won't be!). He was likely hoping no one would notice that as it opens a can of worms that would have taken another 15 minutes to discuss. You asked the right question though.

[@bloodyadaku]

@@chrisorr9029 Thank you for your explanation! Glad I wasn't just misunderstanding something.

[@bhavpreetsinghyt4123]

Love from India ❣️❤️ doin really great

[@MiaLy86]

Hi Professor Leonard, are you going to be uploading any more videos soon? I'm taking differential equations over winter break and I find your videos so helpful but my course covers things like Laplace Transforms and Fournier Series, etc.

[@onemanenclave]

me simple man me see professor leonard video me click like

[@muhammadamjad5284]

Hi Sir, i want to know that we have studied three cases (i) Y gone (ii) X gone (iii) both gone if both x and y appears than what should we do?

[@jackpokrywka542]

What if there’s no y’ lol

[@Woodman34x]

I would like for you to know if Professor Leonard that I forgive you for making the mistake and not having the 1/c in front of the arctan. 20:18. However I do understand the excitement of mathematics. And when you start getting the numbers going you start getting a little crazy, In a good way.

[@dk-xn9el]

Sir u didnt talk about variation of paramaters in second order diff eqns

[@xandersafrunek2151]

Why can you neglect the fact that the arbitrary constant should appear outside of the inv. trig. functions? (i.e) 1/k*arcsin(x/k)

[@rufusli1284]

The integration table should be arcsin(x/k), no 1/k in front of it.

[@hollywoodbanayad7755]

Thank you Professor Leonard ^_^

[@Lestibournes]

Says he's not going to show the chain rule anymore. Proceeds to immediately show the chain rule again.

[@valentin150jb]

A great lecture like always. I have a question. The first example at 49 min could I also divide by "y" and solve it as a separable equation? Thank you for the answer.

[@mohamedabdukadir2361]

thanks prof

[@azngnslngr]

Your videos have been so helpful! Only reason I can do Bernoulli's Equation >_< Would you consider uploading a video on how to do nth-order differential equations? I've watched your videos on the topics that we've covered so far in class, but am pretty confused on n-th order differential equations.

[@nalathekitten3594]

Thanyou so much for everything

[@davidgeorgiev5751]

Feels good having the Man of Steel(Superman) as my calculus teacher :) :D

[@martinsanchez-hw4fi]

why dont you have vidos on higher order differential equations? :(

[@rawanalhashem3647]

Thank you professor, I want to ask about Euler's method, can you make a video about it.

[@icee562]

Man I can't wait till he gets to Series Solutions :D

[@HH-yb2dv]

Hi.. thanks

[@ggman69]

But if I have an x and y mixed term, is it solvable? Such as y'' + f(x) g(y) y' + y = 0

[@jamiec2852]

You've got a ring on your finger now! 8 years later haha

[@vaughnmonkey]

for 26:45 do you not have to distribute the y to both P and dP/dy?

[@henrynwosu6277]

He says we need the chain rule, i see no reason why. I see no reason why we can't carry out separation of variables and integrate after we have replaced dy/dx with P. He says its because there is no X. I don't see how. Hopefully, I am wrong.

[@scorpionedge]

What if both x and y are no missing? How do we solve this?

[@bhavikpansara766]

please start a paid course on online learning platforms (like Udemy, LinkedIn learning, skillshare,...). I would like to join your maths courses. If you have such types of courses already then please share the link of it with me. thanks.

[@erickmorfin1420]

Do you teach elementary linear algebra? Such as matrices, determinants and blah blah blah?

[@johnholme783]

It should be 1/c2!

[@lania4334]

Can you give me a name of a book about partial differential equation

[@actualBIAS]

Please make a comeback at 1Mio Subscribers. You have gained 12k Subs over the last 10 days. Starting from 886 now 898. Calculate the moment of comeback via ODE's

[@doomerman965]

Hey professor can you do a video on exact equations? Please

[@ProfessorLeonard]

coming up next. check back in one week

[@yeifrirodriguez5200]

The boss

[@johnnyarellano7653]

How would I focus with a fine as teacher like him

[@azure.6874]

ikr

[@هنا-ط9خ]

WOOOOOOOOOOOW

[@هنا-ط9خ]

وحشتيني 😭😭😭💔

[@هنا-ط9خ]

أمس كانت مناقشة فوفاا 😂😂 وانتي متى ؟ I can do it 😁

[@حموديالأسودي-ق3ر]

Hi

[@denizbayrak3501]

Hocam daşşak koktu buralar

[@wispeidolon3422]