Integrating factors 1

[gdullard]

3 people cant be taught simple math by god himself

[addieroxrev09]

Bernoulli Method would be useful too.. just a couple of examples would be good. not asking for much. thanks mr.Khan :)

[watscrick]

Why does mu(x) remain mu(x) when you are taking its derivative with respect to y? Additionally, if mu can be a function of x,y, or x and y, how do we know that there isn't a y in the function mu? If there was a y, then shouldn't taking its derivative with respect to y give you something? That part confused me. Also, why didn't Sal do the product rule for the left-hand side (our new M) but did do the product rule with the right-hand side (our new N)?

[arrching]

@watscrick cause the derivative of the left hand mu(x) with respect to y is zero so if you do the product rule, it will be just mu(x)(3x+2y) + (0)(3xy + y^2) so just cancel it out.

[jennybon999]

you make calculus easy <3

[ElectricPhantom]

dude, you're awesome!!!

[prvnpn216]

Sal you are god

[nathiqueeteh]

Please upload Bernoulli Method! :)

[Lavabug]

The differential equations videos seem almost complete, but it needs a few more tricks. Like substitution tricks when even the integrating factor method doesn't work, or the Bernoulli equation method. It would be nice to see them added.

[riebals]

in the end when you get dx/x=dμ/μ if I'm not mistaken you shouldn't say that x=μ, but |x|=|μ| which is not necessarily the same. Picky me lol

[Platemaster]

Maybe I have been studying too much, but I giggle everytime you say "mu"

[amnesiai]

i love this!!!

[CogitoErgoCogitoSum]

When you finished up this video you said that &mu; = x.  What happened to your constant of integration?

[kourosh89]

@CogitoErgoCogitoSum I know this comment is from a year ago, but I have the same question.

[malachispacewanderer]

You are saintly.

[ooebuTuoYoo]

At 7:02 , shouldn't it have become U(x) (x+3y) = .... or am i mistaken? thanks!

[yamenhawit]

thanks! you're the best... But there is a shortcut to finding μ:

μ(x) = e^∫ [(My-Nx)/N]

OR

μ(x) = e^∫ [(Nx-My)/M]

...so in this case it becomes e^∫ (1/X) or e^ln|X| or just X

[mohanjigera]

thanks a lot

[babygurl25392]

thankssssssssss

[padaneis]

@knighttango: for linear equations like this one, an integrating factor always exists, depending on x only: this is way we have a general formula for solving. For the exam: take a look at the Schaum outline on differential equations, which has a lot of exercises and examples. If you are interested in intergating factors by a theoretical point of view (I hope you are:-) ), then Google "Frobenius theorem". (You should know something about differential form for this). Good luck!

[knighttango]

now supposing a get a question for exam to solve a diff equation....

how will i be sure that i can find an integrating factor u(x)??

i mean here the (x+y) got cancelled...what if it was more complex?

[fermixx]

@knighttango : my book reads:

Existance of an integrating factor:

"If a non exact differential equation has a general solution F(x,y) = C, then it has an integrating factor"

So that theorem is just a piece of shit, and i never used it.

We are fucked up..

[mooriel82]

thanks trhanks thanks i have a quiz about this in half an hour and this really helped me !

[jojoh44]

I love your video's, very helpful

[supunnba]

thanks

[calvinhobbesliker2]

Can you use this trick to solve all first order ordinary differential equations?

[furtivefelon]

i don't think so, only a very small class of ODE is solvable exactly.

[JashanSKang]

do u have to assume the right integrating factor until it works?

[JashanSKang]

it doesnt matter whether the integrating function is a function of y or x right? becuase u will get the same answer etiher

[Plutoniummatt]

Excellent

[tijdvooreendansje]

the purple is very friendly on the eyes...you hardly ever use that though. just a thought.