Recent content by chwala

My special thanks to Fresh42, Mark44, Bvu, Perok, SammyS, Haruspex, Orodruin, Chestermiller, WWGD, Martinbn, and the other person from South Africa for the elaborate math discussions over the years. I look forward to a more productive 2026 and beyond! Long live Physics Forums!

Thks @Gavran ,I will check on your approach...

This is the question, I understand the concept, in ##\mathbb{Z_n}## an element is a is a unit if and only if gcd( a,n) =1. My understanding of backwards substitution, ... i have using Euclidean algorithm, ##471 = 3⋅121 + 108## ##121 = 1⋅108 + 13## ##108 =8⋅13+4## ##13=3⋅4+1## ##4=4⋅1+0##...

@Mark i re-uploaded, i too could not see the highlighted part :biggrin:

Thanks for the thoughtful input — actually, I’ve taken this as a personal challenge! I’ll be applying the Runge-Kutta method to this problem and working through it manually as far as possible. I’m also committed to generating more of these hybrid-style problems that push the boundaries of how we...

Ok, i just came up with this ode. How does one go about to solve it? My attempt Let ##M(x,y) =(2xy+\cos y+\dfrac{2y}{x}-\sin x)## and ##N(x,y) = (x^2-y\sin y+1)## ##\dfrac{\partial M}{\partial y}= 2x - \sin y + \dfrac{2}{x}## and ##\dfrac{\partial N}{\partial x}= 2x## Not exact.

The formal solution to me does not look complete, but i fully understand the view of mathematicians coming to that conclusion.

That is exactly, where my problem is. Somehow this should be integrable... hence the reason of the post.

OK let me be specific, how do you integrate $$ \dfrac{1}{x^x e^{-x}}\int 6x. x^x. e^{-x} dx $$

...explicitly post here your integrating factor... @fresh_42 I would like help from this step, otherwise you may want to close this thread. In post 1, I left out the 'e' typo error. Thanks.

##e^{x \ln x - x} = x^x e^{-x}##.

I think we’re just going round in circles without any meaningful progress. In my mind, I’m very clear on where I had reached and where I am stuck. Getting the integrating factor is actually the least of my problems. I already know how to form the integrating factor — and yes, I agree it’s a bit...

Where was it wrong? The missing of the constant ##C##? My understanding is that contant ##C##is embedded on the integral itself as the integrating factor will subsequently multiply out each term of the differential equation.

I thought i already mentioned the last step where I reached, ie finding the I.f ...my problem from that point is solely on how to use the integrating factor to this specifically arrive at the required solution.

Wait, I thought when using integrating factor 'c' is silent or rather not considered... each term ##y', P(x) ## and ##Q(x)## will be multiplied by the integrating factor, with no consideration to your c.