Around 15 minutes, the sec(-pi/4) is not 1/sqrt(2), it's just sqrt(2). It doesn't change the end result at all but dont want any trig students getting confused and messing up a basic question later.
Yea, thanks for pointing it out! I dont think any trig students will be watching this since this is meant to be for diff eq students (or better yet, diff eq teachers lol) : )
@@blackpenredpen i present myself, I'm a trig student xd, and am just now getting into the derivative by definition, but am fascinated by calculus in general and am rather frustrated with how slowly we're going in my calc I class, so I'm watching videos to prepare myself for future material.
this was a great summary of the diff eq solving techniques learned in the abridged diff eq portion of an engineering mathematics course. well done bprp!
Super set of DEs, gradually getting harder, but building on the previous. Well done for making them all so that they all miraculously come to 1 + tan(x)… Bravo!
I was taught for exact differentials that when its verified that the equation is exact, you just take the same equation and integrate it such that: 1) 'y' has to be considered constant inside the 'dx' integral 2) all terms containing 'x' in the 'dy' integral are removed Eg: In the equation he picked, it is confirmed to be exact so-> [(-sinx)y + sinx - cosx]dx + [cosx]dy = 0 =⟩ ∫[(-sinx)y + sinx - cosx]dx + ∫[0]dy = 0 [Since there is no term containing y in dy] =⟩ [(cosx)y - cosx - sinx] = c =⟩ y = (cosx + sinx)/cosx [Since c=0 on putting y(π/4)=2] =⟩ y = 1 + tanx
Thanks for teaching me new differential equation techniques. In my school syllabus the only diff eqs we learn to solve are those dead easy ones which are 1. dy/dx = f(x) 2. dy/dx = f(y) 3. d^2y/dx^2 = f(x) which really doesnt do diff eqns justice.
a) separable , b) Riccati equation c) linear first order d) linear first order e) linear first order f) Bernoulli equation b) is Riccati but it looks like Bessel equation after reduction to second order linear There is type mistake in thumbnali which makes second one Riccati but in fact it is separable or autonomous
14:54 thanks for impressing me hahaha Suppose sec(-pi/4)=1/sqrt(2), sec(pi/4)=1/sqrt(2) as secant functions are even functions We know that sec x = 1/cos x Therefore, cos(pi/4) = (1/sqrt(2))¯¹ = sqrt(2) and cos(pi/4) = sqrt(2) / 2 As sqrt(2)≠sqrt(2)/2, this leads to a contradiction. Using proof by contradiction, sec(-pi/4)≠1/sqrt(2)
Hey I have an interesting question perhaps you could make a video on What would the limit to +infinity be of X^a•e^-a Where a=x^a What what would limit to +0 of x be ? From desmos I figured limit to infinity is 0 and limit to +0 is 1/e but not sure
when a differential equation has an initial condition, why add the +C then solve for it later? it seems like it would be easier to use a definite integral instead (for example integrate from 2 to y on the y side and pi/4 to x on the x side)
J'adore vos vidéos merci beaucoup, juste qu'il faudrait préciser dans quel ensemble on doit rechercher la solution, sinon il y a toujours une solution dans tous les ensembles structurés que l'on peut imaginer, c'est la force du langage mathématique qui n'est qu'une contraction du langage naturel de tous les mortels. MERCI pour vos efforts, c'est superbe !...CONTINUEZ
If i m not mistaken at the first equation you call the result the "general solution" but thats not correct since y=0 is also a solution that s not contained. Nice video as always love you.
14:57. sec(-pi/4) = sqrt(2) not 1/sqrt(2). a easy method to calculate that is: sec(-pi/4) = 1/cos(-pi/4). cos(-x) = cos(x), so 1/cos(-pi/4) = 1/cos(pi/4) = sec(pi/4) = sqrt(2)
I too have an evil differential equation, but alas the solution isn't y=1+tanx. Let a and b be fixed, real-valued constants satisfying b≤a². Find the most general family of real-valued solutions s(t) satisfying the differential equation (ds/dt)² = 4a²s⁴(s²+b)⁻² - s² and interpret this family geometrically.
In the one before the last one Why did you not talk about the right hand side being zero? Does it not matter? Because the left hand side is always secx-secx Is that where the constants come in or what?
Hello, i don't know calculus but in question 2 i tried to take the integral of y by x and got (y^2-2y+2)x=y(x) why can't i do this? Can someone explain if they have the time?
Another great video, however we have to stop talking about C. Anytime we have an arbitrary constant and it’s added or subtracted or any other algebraic operation with another constant , it’s still an Arbitrary constant and we don’t have to keep writing C1,C2 etc. just always write plus C at the end.
A process for finding the signed area between the graph of a function and the x-axis. If the given function is a rate of change, such as speed at every point in time, then the integral tells you the cumulative effect of this rate of change. An application of integration you might be familiar with, is the formulas for the surface area and volume of shapes such as spheres and cones. This is where the 4/3 comes from, for volume of a sphere, for instance. In 7th grade, you just take it as a given, and don't care how we know that. But in Calculus, you would want to know how we determined that formula, as you'd learn how to generalize the process. By "signed area", what I mean is that area above the x-axis is considered positive, and area below the x-axis is considered negative.
Learn integration techniques & differential equations from Brilliant: 👉 brilliant.org/blackpenredpen/ (20% off with this link!)
thanks, I am really happy!!!!
I am gald to know that you uploaded a new video!!!
Thanks for all!!!!
Loves and prayers from Ecuador!!!
不知道設計這份考卷的人是誰
Around 15 minutes, the sec(-pi/4) is not 1/sqrt(2), it's just sqrt(2). It doesn't change the end result at all but dont want any trig students getting confused and messing up a basic question later.
Yea, thanks for pointing it out!
I dont think any trig students will be watching this since this is meant to be for diff eq students (or better yet, diff eq teachers lol)
: )
@@blackpenredpen or people like me who are CS engineers that just like math for fun and watch these while at work xD
@@blackpenredpen i present myself, I'm a trig student xd, and am just now getting into the derivative by definition, but am fascinated by calculus in general and am rather frustrated with how slowly we're going in my calc I class, so I'm watching videos to prepare myself for future material.
@@OpRaven-62 me too I'm still an algebra 2 student but am doing calc on my own :) love bprp's videos
35:05 Good thing cos(π/4) is equal to sin(π/4), otherwise it would have been a glaring mistake.
this was a great summary of the diff eq solving techniques learned in the abridged diff eq portion of an engineering mathematics course. well done bprp!
Thanks!!
I really like these a bit longer videos, i think i prefer this one over the shorter ones
14:57. sec(-pi/4) = sqrt(2) not 1/sqrt(2). Range of sec(x) is |sec(x)| > 1
Ah thanks for pointing that out.
@@blackpenredpen you were lucky that c had to be 0 either way lol
Super set of DEs, gradually getting harder, but building on the previous. Well done for making them all so that they all miraculously come to 1 + tan(x)… Bravo!
Wow.. ur explanation makes things easier.. that anyone can easily understand.. love from Pakistan 🇵🇰🇵🇰 give you big respect..
I was taught for exact differentials that when its verified that the equation is exact, you just take the same equation and integrate it such that:
1) 'y' has to be considered constant inside the 'dx' integral
2) all terms containing 'x' in the 'dy' integral are removed
Eg: In the equation he picked, it is confirmed to be exact so->
[(-sinx)y + sinx - cosx]dx + [cosx]dy = 0
=⟩ ∫[(-sinx)y + sinx - cosx]dx + ∫[0]dy = 0
[Since there is no term containing y in dy]
=⟩ [(cosx)y - cosx - sinx] = c
=⟩ y = (cosx + sinx)/cosx
[Since c=0 on putting y(π/4)=2]
=⟩ y = 1 + tanx
I learnt something very valuable today.
Thank you Mr BPRP !
Thanks for teaching me new differential equation techniques. In my school syllabus the only diff eqs we learn to solve are those dead easy ones which are
1. dy/dx = f(x)
2. dy/dx = f(y)
3. d^2y/dx^2 = f(x)
which really doesnt do diff eqns justice.
This looks fun to put on an exam and freak out the students.
This is perfect review for me as my finals are next week!!! 🎉
Masterpiece channel
a) separable ,
b) Riccati equation
c) linear first order
d) linear first order
e) linear first order
f) Bernoulli equation
b) is Riccati but it looks like Bessel equation after reduction to second order linear
There is type mistake in thumbnali which makes second one Riccati but in fact it is separable or autonomous
14:54 thanks for impressing me hahaha
Suppose sec(-pi/4)=1/sqrt(2), sec(pi/4)=1/sqrt(2) as secant functions are even functions
We know that sec x = 1/cos x
Therefore, cos(pi/4) = (1/sqrt(2))¯¹ = sqrt(2) and cos(pi/4) = sqrt(2) / 2
As sqrt(2)≠sqrt(2)/2, this leads to a contradiction. Using proof by contradiction, sec(-pi/4)≠1/sqrt(2)
Nice use of Clairaut's theorem for the exact differential equation
Hey I have an interesting question perhaps you could make a video on
What would the limit to +infinity be of
X^a•e^-a
Where a=x^a
What what would limit to +0 of x be ?
From desmos I figured limit to infinity is 0 and limit to +0 is 1/e but not sure
I really miss the lovely wizard beard.
Sadly the beard gone
But the wizard stays
Super. Oglądam Twoje filmy. Pozdrowienia z Polski!....Super. I watch your films. Greetings from Poland!
No matter the result, there are many ways to get there.
Some more difficult than others.
Teacher ...
*You're almost achieved your goal.... One Million subscribers* ....
*Congratulations*
*bP🖋rP🖍* ❤
when a differential equation has an initial condition, why add the +C then solve for it later? it seems like it would be easier to use a definite integral instead (for example integrate from 2 to y on the y side and pi/4 to x on the x side)
That's awesome! Thank you very much
Your loyal student from Syria 💙
Yes, you are right.
J'adore vos vidéos merci beaucoup, juste qu'il faudrait préciser dans quel ensemble on doit rechercher la solution, sinon il y a toujours une solution dans tous les ensembles structurés que l'on peut imaginer, c'est la force du langage mathématique qui n'est qu'une contraction du langage naturel de tous les mortels. MERCI pour vos efforts, c'est superbe !...CONTINUEZ
SO CLOSE TO 1M!
Can you find the radius of the circle which touches the Latus rectum , axis and circumference of the parabola Y²=4aX
If i m not mistaken at the first equation you call the result the "general solution" but thats not correct since y=0 is also a solution that s not contained. Nice video as always love you.
blackpenredpen solves everything.
6 diff eqs
less go
Love you my math gem.
14:57. sec(-pi/4) = sqrt(2) not 1/sqrt(2). a easy method to calculate that is:
sec(-pi/4) = 1/cos(-pi/4). cos(-x) = cos(x), so
1/cos(-pi/4) = 1/cos(pi/4) = sec(pi/4) = sqrt(2)
3:31 Are you sure the c belongs there? Doesn't that restrict the values it can take on?
I too have an evil differential equation, but alas the solution isn't y=1+tanx.
Let a and b be fixed, real-valued constants satisfying b≤a². Find the most general family of real-valued solutions s(t) satisfying the differential equation
(ds/dt)² = 4a²s⁴(s²+b)⁻² - s²
and interpret this family geometrically.
Now put them all on a test and confuse your students
Wow, nice video. The fact that everything just ends up being tan(x)+1 made me laugh LOL😂
do a video on how:
-i is equal to 1/i
but (-i)^2 == 1 while (1/i)^2 == -1
This man is a madman and that why I follow him
Wow, you're amazing!
35:23 you accidentally put in a cos(x) where it’s a sin(x), but you didn’t notice since when x=pi/4 both answers are the same.
Ahh. Thanks.
If dy/dx = (3yx^2)/(x^3 + 2y^4)
Find the solution of the differential.
y(2)
brilliant
In the one before the last one
Why did you not talk about the right hand side being zero?
Does it not matter? Because the left hand side is always secx-secx
Is that where the constants come in or what?
When I become a math teacher, I'm going to make a test of JUST these questions. :D
Just waiting for your 1000^2 subscribers :)
Thanks!!!
Do you have any hardest problems?
Try integrate sin(x)*sin(x*x)
i love it!
What, no solution involving Laplace transformations? :P
😆
Why is this video unlisted?
35:03 2cosines,bruh
Amazing)
sir can you help me solve 2x^3y’=y(y^2+3x^2) using y=xv homogenous? thanks a lot
Bravo
when you at the opps math class and you hear them say "pass bro the evil differential equation quiz"
i need one of those t-shirts or the graphics file of the text
looking fwd 2 some1 making the 7th question with ans 1+tanx
Are you create this video uc barkely University
at 30:00 i broke up. i hadn't learned that yet!
Hello again
@@ronin4923 Hi~ Have you heard about the 13-year old who watches differential equation videos? LOL
Hey bprp, how can i solve 2^x=2x
I just had a calc exam with this question:
Show that x + sin(x) = 0 only has one solution
I spent an hour on that and don’t think i got it right
Hello, i don't know calculus but in question 2 i tried to take the integral of y by x and got (y^2-2y+2)x=y(x) why can't i do this? Can someone explain if they have the time?
What is there better than 6 DEs? 12 DEs!
how about 24 DEs?
it's done here: ruclips.net/video/e-cTygNbEUE/видео.html
@@blackpenredpen Excellent 😃
He be black pening and red pening
7:14 tanc=0 => c=kπ , k is an integer. Why did you not care other solutions?
You could say the same thing for all the solutions, and every time a trig function is written out
put that on the test and students will doubt their life on the sol.
No Picard iteration!?
happy halloween.
Same to you!
@@blackpenredpen yay 1million subs sooooon
@@blackpenredpen Same for both!!!!!
I’m starting to think that y = 1+tanx
wouldn't it be nice
I hope my future professor watch this and use it as a test lol. I'm a freshman btw
y!=x!. PLZ GRAPH
Another great video, however we have to stop talking about C. Anytime we have an arbitrary constant and it’s added or subtracted or any other algebraic operation with another constant , it’s still an Arbitrary constant and we don’t have to keep writing C1,C2 etc. just always write plus C at the end.
I have to be honest, I love you as my make believe calc teacher, but if i had a choice, i wouldnt touch your class unless I was a mathematics major.
can someone please help me understand why this proof is wrong? -8 = (-2)^3 = ((-2)^2)^3/2 = (4)^3/2 = 64^1/2 = 8. so -8 = 8? please help :D
I think the proof is wrong because in step 2 the /2 should also be cubed and -2 sqquared is 4 and not -4
well
Oh! Not that hard but EZ! lol!
Can you define integration to 7th grade student
A process for finding the signed area between the graph of a function and the x-axis. If the given function is a rate of change, such as speed at every point in time, then the integral tells you the cumulative effect of this rate of change. An application of integration you might be familiar with, is the formulas for the surface area and volume of shapes such as spheres and cones. This is where the 4/3 comes from, for volume of a sphere, for instance. In 7th grade, you just take it as a given, and don't care how we know that. But in Calculus, you would want to know how we determined that formula, as you'd learn how to generalize the process.
By "signed area", what I mean is that area above the x-axis is considered positive, and area below the x-axis is considered negative.
ive solved harder ;)
Bro said difficult and solves ncert differential equations
I am sorry
I think you speak too fast😭