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Cauchy-Euler differential equation
MM-10.4-8
Solve the Cauchy-Euler differential equation
(x + 1)^2 d^2y/dx^2 + (x + 1)dy/dx + y =4(cos ln(x + 1))^2
#differential_equations #cauchy #euler #cipher
Solve the Cauchy-Euler differential equation
(x + 1)^2 d^2y/dx^2 + (x + 1)dy/dx + y =4(cos ln(x + 1))^2
#differential_equations #cauchy #euler #cipher
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Відео
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Переглядів 1627 годин тому
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Переглядів 1317 годин тому
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Переглядів 1967 годин тому
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Переглядів 1059 годин тому
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Переглядів 2329 годин тому
Find the exact value of sin(37π/144).sin(13π/72).sin(35π/144).sin(11π/72)
Sweet
i'd like to know how you evaluate the digamma(1/2) and digamma prime of 1/2
i mean the part when the digamma function apears and you substitute for euler mascheroni and natural log part, where did that come from?
These results were applied directly. Please go through the following links under the topic special values en.wikipedia.org/wiki/Trigamma_function en.wikipedia.org/wiki/Digamma_function
I'm not studying on such a high level of calculus but l can't understand what the B function that you use on 3.30.Can you please explain?
We have used Beta function. Please go through the following link. en.wikipedia.org/wiki/Beta_function
Beautiful! I am going to read up on the beta function now!
how much time do you spend daily doing all this?
great
Excellent
Nice, but you should also have shown the conditions for them to apply.
Could you do video on proving beta function?
I already have a video ua-cam.com/video/KN2EaIndlpc/v-deo.html
@@cipherunity thanks
@@jasimmathsandphysics You are welcome
That's a great formula you proved ❤
Thanks
Keep up the good work bro , subscribed :)
Thanks
Hang on! This is a JEE integral? Isn't it?
May be. Do you have a reference?
@@cipherunity Yeah it is, it's a JEE advanced integral.This can be solved using beta functions as well.
@@Dedicate25 Let us see if I can do it using beta function.
Nice! 😃
Thanks
Excellent
Thanks
Hello... I have a question and I hope you can help me. My question is that I would like to learn mathematics in order to study classical physics and quantum physics. Do you have courses, UA-cam channels or resources where you learned math from algebra to calculus? This was my question and I hope you can help me ❤.
I have about 4750 videos covering algebra, calculus, trignometry, limits and continuity, differential equations, Fourier series, Laplace transform and number theory. All these videos can be helpful.
👍
I already have a video about that in which I combine sine, cosine and tangent function. I deleted that video. You shall see now 3 videos
What software do you use for presenting these?
Microsoft office (Word + Power point)
@@cipherunity i thought it was only powerpoint, i am curious what you use word for
@@qwertyman123 You need to type every thing in word. Then it is transfered to power point.
Excellent
Mental integral
π / √φ Φ is golden ratio.
Excellent
Excellent
How about Int_0^pi/4 (1+tan^2 t) d(tan t)= ( tan t + tan^3 t /3)_0^(pi/4) = 1+1/3=4/3
Excellent
Good stuff
A nice video would be: Prove arcsin a + arcsin b= ; and arccos a +arccos b =.
I might have done it already. I shall check
It can be quite long but it can be calculated with Ostrogradski's method of isolation rational part of integral
I see
Quick question if you change the bounds from 0 to infinity to 0 to 1 does this technique still work? You can’t add the two integrals when there bounds are different?
Nah bound should be same
I shall look into it
Hello... How can I contact you because I have some questions about learning mathematics and I hope you can help me?
Nice question
Yes it is
How can i send an integral question for you? Its national contests
You can post it here. I may or may not be able to solve it.
I could do that one
Very good
My first Olympiad problem was of this type lol.
I remember struggling with this kind of Diophantine equations and then i discovered that they're in a class called "Mordell's equations". The way to prove there are no solutions using the technique I saw in the file i downloaded is to find a way to factor the expression and get a contradiction by quadratic reriprocy and I'm pretty sure this problem was in that file y²=x³+23 y²+4²=x³+3³ y²+4=(x+3)(x²-3x+9) it's easy to see that x must be odd and x=1(mod 4) and to get those claims just look at the original equation modulo 4. With this we get that x²-3x+9=3(mod 4) so x²-3x+9 must contain a prime factor p=3(mod 4) so looking at the equation modulo p you get y²+4=0(mod p) so y²+1=(mod p) but p=3(mod 4) and it is well known that this case has no solutions by quadratic reciprocy.
If a is even then 3a²-1 is going to be -1 modulo 4 which is a contradiction. If a is odd then 3a²-1 is going to be -1 modulo 3, contradiction.
Wait why do we get n|x+1?
Just think. You shall know the answer. Keep in mind 2 is a prime number.
The solution makes sense and i even get the feeling that everything is obvious but coming up with the idea is the hard part :(.
I still have a long waaaay to go in NT huh...
Yeah my aprooach was the second solution. x³ is only congruent to 0,1 or -1 modulo 9 and if none of the numbers a,b or c is divisible by 9 we'll get a contradiction because a³+b³+c³ will only be congruent to 3,1,-1 and -3 modulo 9.
Fantastic evaluation. Beta and Gamma functions make everything so interesting.
Right
Nice
Thanks
I solved more simplify. On one of start step we can subs 1/x+arctgx =t ===> dt = 1/(1+x^2) - 1/x^2 = (-1) /(x^2*(x^2+1)) and interval from 1+π/4 to π/2. At result we have int dt/t = ln t = ln (2π/4+π) 🎉
Fantastic
Thanks
This sum is very sneaky, and it only takes the McLaurin's expansion of exponential to compute it. This is so cool!
That is correct.
At 0:57 B is missing. It should be B(1/4, 3/4) and B(1/4, 1-1/4). Sorry for this mistake
yess
Thanks a lot for rendering premium content to free of cost . May God bless you
God bless you too.
What's the name of background music?
" Desert caravan " by Aaron Kenny
Thanks a lot, love your videos because I learn a lot from them
@@Kairavrathi You are welcome.
How did you thought of that substitution
Fantastic evaluation. Please discuss the other methods of evaluating this integration.
It is done