A Homemade Non-Linear Differential Equation
HTML-код
- Опубликовано: 17 сен 2024
- 🤩 Hello everyone, I'm very excited to bring you a new channel (aplusbi)
Enjoy...and thank you for your support!!! 🧡🥰🎉🥳🧡
/ @sybermathshorts
/ @aplusbi
❤️ ❤️ ❤️ My Amazon Store: www.amazon.com...
When you purchase something from here, I will make a small percentage of commission that helps me continue making videos for you.
If you are preparing for Math Competitions and Math Olympiads, then this is the page for you!
CHECK IT OUT!!! ❤️ ❤️ ❤️
❤️ A Differential Equation | The Result Will Surprise You! • A Differential Equatio...
❤️ Crux Mathematicorum: cms.math.ca/pu...
❤️ A Problem From ARML-NYSML Math Contests: • A Problem From ARML-NY...
❤️ LOGARITHMIC/RADICAL EQUATION: • LOGARITHMIC/RADICAL EQ...
❤️ Finding cos36·cos72 | A Nice Trick: • Finding cos36·cos72 | ...
⭐ ⭐ Can We Find The Inverse of f(x) = x^x? • Can We Find The Invers...
⭐ Join this channel to get access to perks:→ bit.ly/3cBgfR1
My merch → teespring.com/...
Follow me → / sybermath
Subscribe → www.youtube.co...
⭐ Suggest → forms.gle/A5bG...
If you need to post a picture of your solution or idea:
in...
#radicals #radicalequations #algebra #calculus #differentialequations #polynomials #prealgebra #polynomialequations #numbertheory #diophantineequations #comparingnumbers #trigonometry #trigonometricequations #complexnumbers #math #mathcompetition #olympiad #matholympiad #mathematics #sybermath #aplusbi #shortsofsyber #iit #iitjee #iitjeepreparation #iitjeemaths #exponentialequations #exponents #exponential #exponent #systemsofequations #systems
#functionalequations #functions #function #maths #counting #sequencesandseries
#algebra #numbertheory #geometry #calculus #counting #mathcontests #mathcompetitions
via @RUclips @Apple @Desmos @NotabilityApp @googledocs @canva
PLAYLISTS 🎵 :
Number Theory Problems: • Number Theory Problems
Challenging Math Problems: • Challenging Math Problems
Trigonometry Problems: • Trigonometry Problems
Diophantine Equations and Systems: • Diophantine Equations ...
Calculus: • Calculus
Will you please provide a PDF of difficult maths problems ?
I love you ❤
Nice!
Thanks!
Please sir❤❤
I am 42 years old. And i loved maths when I was younger, and your videos make my love for maths to another level.
I'm glad to hear that! Thanks for watching 😍
@@SyberMath You are the best. Best wishes from an Indian from Dubai. I have watched all your videos. And this brings a lot of joy to me. Thank you so much.
Hello sir
If c=0? That value is missed. If c=0, that integral is -1/y=x+k...
That is a known result!
(y')'=(y^2)'...y'=y^2+c,..dy/(y^2+c)=dx...(1/√c)arctg(y/√c)=x+C1...y/√c=tg(√c(x+C1))
Have you replaced y in terms of his solution?
what if c
You didn't consider the cases c=0 and c
trivial cases. y = 0
👍✌️☮️😀😀☮️✌️👍
😁😍🥳
problem
y" = 2yy'
Note:
d(y²)/dx = 2yy'
and by definition
y" = d(y')/dx
Setting these equal we get
d(y')/dx = d(y²)/dx
Integrate.
∫ d(y')/dx dx = ∫ d(y²)/dx dx
∫ d(y') = ∫ d(y²)
y' = y² + C₁
, where C₁ is a constant of integration.
dy/dx = y² + C₁
dy / (y² + C₁) = dx
Integrate a second time.
∫ dy / (y² + C₁) = ∫ dx
1/C₁ ∫ dy / (1+y²/C₁) = x + C₂
, where C₂ is a constant of integration.
Substitute
z = y/√C₁
z√C₁ = y
√C₁ dz = dy
1/C₁ ∫ √C₁ dz / (1+z²) = x+C₂
1/√C₁ ∫ dz / (1+z²) = x+C₂
1/√C₁ tan⁻¹(z) = x+C₂
1/√C₁ tan⁻¹(y/√C₁) = x+C₂
tan⁻¹(y/√C₁) = √C₁ (x+C₂)
y/√C₁ = tan[√C₁ (x+C₂)]
y = √C₁ tan[√C₁ (x+C₂)]
answer
y = √C₁ tan[√C₁ (x+C₂)]