INSANE 15 MARK Differential Equations Question | A Level Maths

[@zubair9081]

Cheeky ‘I understand it now’ reference Neil NOICE

[@NeilDoesMaths]

hahahaha NOICE

[@vybs9235]

The fact that i did everything till the constant part in my head gives me such a confidence boost

[@chamidumadumal7130]

Hey Neil, I have two questions. First: 6:29 why didn't you consider the modulus of tan u? You made a big deal about the root of a square being the modulus but you seemed to glaze over it when taking the root of tan square. Could you please explain why? Second: In the question it is given that x,y>0. When you substitute x=sec(u) you lost part of the domain from 0 to 1 because sec function has no values in this range but x could (eg: x=0.5 is perfectly valid but sec(u)= 0.5 has no real values). How is this justified?

[@isaacto8761]

I can see immediately that 1 is likely not a problem, because the sign for the x side and for the right side needs to be the same, and they likely cancel out making the modulus unnecessary. But I don't see an immediate justification for 2.

[@pratyushpandya1655]

I'm a 15 year old learning quadratics in school and watching how to solve differential equations at 1 am 💀💀

[@ahandas3299]

I thought I was the only one

[@NeilDoesMaths]

this is the best way to spend your night! Hopefully you found it entertaining haha

[@alguem24]

4 days ago I would've said same

[@suryanshu8692]

It's easy

[@mista5796]

You would have to be told to do this substitution in the exam. There isn’t enough time to brute force all possible substitutions through and you can’t rely on just getting lucky first time. If you have the luxury of time, then you can try different substitutions to see which work. But chances are you’ll try a few until you find one that does work.

[@GrowTube170]

Amazing, it was smooth flowing, I enjoyed it all through.

[@wallythe-k4036]

Everything’s fine except the question should write “x > 1, y > 1”, you know the numerator and denominator might be negative otherwise.

[@syed3344]

@@wallythe-k4036 it is already assumed they r in the domain

[@alanclarke4646]

It says they are both > 0 IN THE QUESTION, so we already know that neither can be negative.

[@wallythe-k4036]

@@alanclarke4646the IVP question is wrong in the sense that when x = 1, in the denominator x^4 - x^2 = 0, so the domain doesn’t even make sense. The question has to be written with restrictions “x > 1, y > 1”. Another clue is that you try to plug in x = 0.5 into the function solution, the y isn’t even real, but a solution has to satisfy the IVP on all values of (x, y) in the given domain, but it can’t! The question itself has to be wrong!

[@syed3344]

@alanclarke4646 lol what they can be negative,by ur logic a biquadratic is always postive 😂

[@aryahan4976]

this is superb, love ur videos!

[@Henry.Bt17]

Actually a beautiful question, just started year 13 doing maths and further maths so cant wait to solve questions like this and harder in the future

[@NeilDoesMaths]

Boootiful question. You've got this dude keep up your hard work 💪🏽

[@samuelmartins2680]

Yoooo me too, solving it makes you feel like a genius 😭😭

[@keithjones9054]

Questions like this separate the special talent from the excellent. It's what make the grades at the end of the day. Even if you can't complete the full solution, you can still get a lot of credit for partial solutions

[@NeilDoesMaths]

Agreed! Noicéè

[@CR7inUefaCristianoLeague]

The thing is can we not substitute like x= 2 in the final answer? I mean its better we write the denominator as s function if we consider

[@coinden3089]

I literally screenshotted the thumbnail of this video and did the entire thing on my phone lol

[@NeilDoesMaths]

Did you get it correct?

[@coinden3089]

@@NeilDoesMaths yeah i got it correct

[@muhammadihsansaladin1056]

​That may be coincident 😂@@coinden3089

[@owen7185]

Awesome demonstration, I am 45 and doing self study

[@gamemakingkirb667]

7:47. You could have solved for C from the arcsec stage; there wasn’t any point to switching to arccos. I think it’s cool to see more math, but you should point out that it isn’t necessary to solving the problem

[@NeilDoesMaths]

Many ways to solve a problem, you don't need to explain every method the video would be 3 hours long g

[@hypershadow4643]

I’m a 15 year old learning integral calculus in class and watching how to solve differential equations at 1121 PM 💀

[@NeilDoesMaths]

I respect it!

[@tanelkagan]

Very well explained - to the extent that the most confusing thing was you breaking out the weird French accent at 0:42 and then promptly dropping it 😅😅

[@NeilDoesMaths]

Hahaha I am 30% french to be fair

[@Christy..1]

isnt i/(x*root(x^2-1) the derivative of negative cosecx ?

[@SKV_8]

the negatives would cancel out on both ends so he just negated them, i too was a little confused but because of the symmetry in the x and y terms the way he did it works but just skips over a small step

[@owen7185]

You have my subscription sir

[@NeilDoesMaths]

Thank you Owen... Glad to have you part of our community 💪🏽

[@withertechz3855]

The question is incorrect as for 0

[@pnachtwey]

I would use RK4.

[@jaysn1683]

Why not substitute x for sinh u, am I the only one to find hyperbolics easier than non cos/sin trigs?

[@NeilDoesMaths]

This is normal maths not further

[@jaysn1683]

Thanks for the insight, I guess different countries teach different things at different times :)

[@ilovemyma7112]

That is just great stuff

[@NeilDoesMaths]

Thanks you Ma

[@delete7316]

Words cannot describe how beautiful this video is.

[@NeilDoesMaths]

Boootiful to the power of bootoful

[@sabanali4093]

I took y²common then x² and seperated em.... Got perfect integral of sec

[@syed3344]

This is supposed to be hard?

[@adandap]

It's a high school level problem, so it's hard by that standard.

[@syed3344]

@adandap still no,am in high school and can give way harder problems than this

[@adandap]

@@syed3344 Good for you

[@NeilDoesMaths]

Stop the cap my guy nobody is falling for it 🤣

[@syed3344]

@@NeilDoesMaths buddy u think am lying?then solve this question: Int(0 to 1) of (xln²x)/(1-x⁴)=k(1+1/3³+1/5³...) find k,this is a high school problem u can't use college maths here

[@alexchan4226]

y = sqrt（(y^4 - y^2)/(x^4 - x^2)）x

[@Gunslinger-us1ek]

amazing

[@NeilDoesMaths]

You're welcome!

[@1985jamesward]

Multiply through by dx. Bye. Lad doesn’t know chain rule

[@arjithbinu9377]

This is at maximum a 5 mark question

[@safestate8750]

I guess I am a part of the 0.1%

[@Paradodger12]

I understand it now

[@NeilDoesMaths]

😎

[@technicallightingfriend4247]

Cos(arccos(1/x) -π/6) Why you multiple cos as number

[@NeilDoesMaths]

I used the addition rule for cosine

[@dan-florinchereches4892]

All the trig substitutions are giving me a headache. Why overxomplicate it and not just use Eulers third substitution. Let (x+1)t=√(x-1)(x+1) t^2(x+1)^2=(x-1)(x+1) Divide by x+1 so xt^2+t^2=x-1 x=-(t^2+1)/(t^2-1) => √(x^2-1)=(x+1)t=(-(t^2+1)/(t^2-1)+1)t=-2t/(t^2-1) dx=(-2t(t^2-1)+(t^2+1)*2t)/(t^2-1)^2dt dx=4t/(t^2+1)^2dt Putting it all together the 1. 4t. 4 --------------------* ------------ dt=---------dt -t^2-1 -2t (t^2-1)^2. t^2+1 ------- * ----------- t^2-1. t^2-1 Which is 4arctg(t)=4arctg(√(x-1)/(X+1))+c