A Homemade Non-Linear Differential Equation

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Опубликовано:

17 сен 2024

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Комментарии : 19

@user-vm7wh6eb7f День назад

Will you please provide a PDF of difficult maths problems ?

@user-vm7wh6eb7f День назад

I love you ❤

@scottleung9587 День назад

Nice!

@SyberMath 22 часа назад

Thanks!

@user-vm7wh6eb7f День назад

Please sir❤❤

@kuriana100 21 час назад

I am 42 years old. And i loved maths when I was younger, and your videos make my love for maths to another level.

@SyberMath 21 час назад

I'm glad to hear that! Thanks for watching 😍

@kuriana100 21 час назад

@@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.

@user-vm7wh6eb7f День назад

Hello sir

@jesusalej1 День назад

If c=0? That value is missed. If c=0, that integral is -1/y=x+k...

@jesusalej1 День назад

That is a known result!

@giuseppemalaguti435 20 часов назад

(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))

@jesusalej1 День назад

Have you replaced y in terms of his solution?

@vladimirkaplun5774 День назад

what if c

@icebear771 День назад

You didn't consider the cases c=0 and c

@FisicTrapella День назад

trivial cases. y = 0

@phill3986 День назад

👍✌️☮️😀😀☮️✌️👍

@SyberMath 22 часа назад

😁😍🥳

@Don-Ensley День назад

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)]