Separable Differential Equation (introduction & example)

I know it doesn't matter, but c can be more than just pi/4.

Can you prove that any function with two separate inputs x and y can be represented as a product of a function of x and another function of y?

Without such a proof I do not feel able to disregard the possibility of a function sufficiently complicated to make such a separation impossible. If a proof is too complicated perhaps you could demonstrate a few examples that don't seem obviously separable, such as (ln|x+y|)^sin(x-y).

blackpenredpen ily

I can prove you can't solve any dif equation with this form y'+ln|sinx|y = g(x) simple the special integration factor is non-algebraic

The piano playing in the background is the secret behind building a math genius.

just stumbled across this video. Amazing explanation but had a question hopefully someone can answer. Isnt the tan of -1 = 3pi/4? I mean its -pi/4 too but its also 3pi/4. Does it matter which one we take? Thanks

looked at the video, but I can't find a solution for my problem , don't find how to separate them.
y' = exp(-y/x) + y/x ==> How do i solve this,, probably simple solution but can't find it ......
tried by playing with ln(y') = (-y/x + ln y/x)
but then how to integratie to find Y ??
greetz

how do u get tan inverse from 1 over 1 + y square?

Why isn't the general solution y = tan( (x^2)/2 + C_1 ) + C_2 ?

Did you do one where there is dy/dx on both sides like this y-x dy/dx = 3-2x^2 dy/dx? Where is it?

It's actually not that bad 😂😂




I'm glad to u

great

This was extremely helpful. THANK YOU

I'm struggling with what feels like some ambiguity here: arctan(y)=1/2 x^2 +c. I'm used to arctan only taking values from - to +pi/2, but the RHS can clearly take a much larger range of values. If we consider arctan +n(pi), does that not create ambiguity for equality when taking tan of each side?

Brilliant review. Just what I needed.

C is actually infinitely recurring since tangent is periodic. C = -pi/4 + pi•k, where k is an integer.

you describe everything so clearly that even watching at double speed I can follow everything

What about this example
(x^2-y^2)y'=x-y

where did tan^-1 comes from

Fantastic

Very cool thanks

I passed my Integral Calculus subject with the help of ur videos. Help this will help me as well. thank u :)

Found ‘em

Using the identity tan(θ+kπ) = tanθ
You should be able to write a general solution given initial condition y(0) = -1

Thank you so much. Tomorrow is my midterm exam. You helped me too much.

Thank you !!!! :-)

Thank you for the calc help :)

I have an equation can you pls send me your email address

I love how you can tell he enjoys what he is doing so much.

tan^-1 it's arctan?

Thank you so much for the Diff Eq series!! I've learned so much more in this 9 minute video than I have in watching 50 mins of my professor talk.

thanks for the help

Can anyone explain me, He wrote 'y(0)=1' in the thumbnail and he's putting the initial condition at 'y(0)= -1 ' like wtf?

🔥

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King

Why C is not 3pi/4? Or 7pi/4

dude you are an absolute beast!

you are perfect🙏🙏🙏🙏🙏

Good day can i help please 🥺 in this equation
dz-(4x³-4x³z+x³z²)dx+(4y-1)(2-z)²dv=0

Good day can i help please 🥺 in this equation
How to find separable Differential equation
dz-(4x³-4x³z+x³z²)dx+(4y-1)(2-z)²dv=0

amazing

What about (3pi)/4?

I can't stop smiling

Excellent!

The way you multiply the dx is not the right way because it is not a number it is a operator. So how you can multiply by operator on both sides