Method of Integrating Factor

In this video, I showed how solvee a differentiiall Equaatiion usinng thhe mmethodd of innteegraating ffactor.

[@shemajwang2866]

The fact that you smiled the whole time made the problem easy😊

[@bassamaman]

you literally have the clear best most satisfying explanation for everything thank you

[@calebbiesinger6844]

This is the energy I need in my life. Thank you prime newtons

[@punditgi]

Prime Newtons knows how to factor in great teaching while integrating, which differentiates him from all the others! ❤🎉😊

[@ruthainmuteba865]

Thank you. You made me unclocked another stumbling block with the Linear Equation.

[@quillingwithtina5505]

this was so helpful thank you so much!

[@user-yb2sf8gx9y]

simplicity makes maths nice

[@GABADIYA_ZA-yv2tc]

i was also smiling through the video😃

[@benjaminharrisiv650]

thanks for making math easy

[@kingbeauregard]

I took differential equations a looooong time ago, and I remember being confused by exact equations. It's nice to be able to revisit the topic and actually understand the integrating factor: the equation didn't start out as exact, but multiply it by the integrating factor and it becomes exact. For the integrating factor to work, every term on the left side of the equation needs to have y or y' in it, right? I seem to recall (it is a very dim memory) that you have to go to extra trouble if there are any terms on the left that don't have some sort of "y" in them. Just move them to the right side of the equation to make life simpler, right?

[@PrimeNewtons]

Yes. Writing the equation in standard form removes all the confusion and sets it up for easy integrating factor multiplication. That way, you don't have any doubts. y' + P(x)y = Q(x) for 1st order.

[@johnnolen8338]

I was never taught this method for solving ODEs. 😥 Would have saved me hours of plug and grind calculations I suspect.

[@AlphaCrucis]

Can you explain variation of parameters? I never understood what's going on intuitively. It just seemed like some magic method.

[@abdulaimohammedsadat-deen4705]

❤❤❤❤❤❤

[@2R2Y2X2]

ty

[@pajthefaj9396]

You should derive the integrating factor to show where it comes from

[@PrimeNewtons]

I'll consider that. Thanks 😊