Solving Separable First Order Differential Equations - Ex 1

preview_player
Показать описание
THERE IS A MISTAKE IN THIS VIDEO; CHECK OUT THE COMMENTS! SORRY!
Solving Separable First Order Differential Equations - Ex 1. One complete example is shown of solving a separable differential equation.
Рекомендации по теме
Комментарии
Автор

The e cancels out the ln on both sides and the 1/2 is the exponent in the ln function, therefore the final answer on the right side should be y= SQRT of (x^(2)+1) * e^c

AhmedAlhafid
Автор

You have literally helped me countless times through out my college life, you explain things better then anyone online, its clear and straight to the point. I hate when I'm stuck and I cant find a video of yours explaining it. Thank you so much.

_Parachini_
Автор

ops yes u are right!
i tried to do too much at once!
thanks for pointing out my mistake!!

patrickjmt
Автор

Wouldn't the e cancel the natural logarithm in

davidirizarry
Автор

the algebra at the end is not correct. there should be no natural log in the final answer. either that, or i need to go back to algebra 2 class.

magaliebravo
Автор

i added annotations pointing out my mistake and gave you credit!
thanks again!

patrickjmt
Автор

1: e^ln(x^2 +1) = x^2+1 and 2: e is a definite constant and C is an arbitrary constant hence e^C is also an arbitrary constant. It can be left as C.

amanmahendroo
Автор

Isn't the answer y = sqrt(x^2+1)*exp(c)... NOT y= In(sqrt(x^2+1))*exp(c)

fan-yang
Автор

The final answer should have y by itself, not |y|. So the answer should be y=±A√(x²+1), which could be left as y=c√(x²+1) where c is any constant.

rachelharas
Автор

When dealing with natural logs, you can bring coefficients up to the exponent inside of the natural log. For example, 2ln(x) = ln(x^2). So with the video example, (1/2)ln(x^2+1) = ln((x^2+1)^(1/2)). anything to the (1/2) power is taking the square root of a number or function.

TheSonofalich
Автор

you cant win 'em all.

i have another video where i reverse the image, so it looks like i use my right hand. would that help?

patrickjmt
Автор

@Username93611 i have used a bunch of different mics - not too happy with any of them. i think i need some anti-aliasing on the new ones

patrickjmt
Автор

I watched PatrickJMT videos for my undergrad engineering courses. 12 years later I come back because of my graduate courses. Time seems nonlinear. Anyways, thank you!

actraveler
Автор

@illisanantexico no need at all apologize :) some of the videos do have mistakes and someone needs to point them out! feel free to comment any time

patrickjmt
Автор

Best tutor ever! Nobody could explain this properly!!!

jyamijuice
Автор

I kid you not, man, I was stuck on the problem (x^2 + 1)dy/dx = -xy.
Then I came here and the first example is almost exactly the same LOL

poopipeboy
Автор

this man got me through college and now hes getting me through my FE exam, 10/10 teacher thanks Patrick

coletallman
Автор

@blackyurizan about this problem, or about math, or about life in general. cause if you are talking about life in general, i am with you on that.

patrickjmt
Автор

i think you should have deleted the ln in both side :/ ?

mohamedakl
Автор

@FrauLahnstein well, these are supplements and not meant to be a 'stand alone' lecture on the topic. any text book on the matter should explain it.

patrickjmt