Solving First order linear differential equation

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In this video, I showed how to use an integrating factor to solve a 1st order differential equation. Thanks to those who observed the mistake in the earlier version of this video. Your help is immensely appreciated.

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Love this professor. Never stop teaching, because those who stop teaching, stop living.

nihil

I feel myself vey lucky my 12th is going on and i got your channel

Legend-nwjh

9:25 hey! I love your videos, im currently bingewatching them all! The calm voice and amazing descriptions are simply the best. I just have a note to say here! Integrating d(xy) would still yield a constant. We just typically dont write it because if you think about it,
f(x)+d = g(x)+c
Is the same as
f(x)= g(x)+c-d
c-d is still a constant so we usually just shorten this step and set the “c-d” to just be +c on the right hand side, so technically your justification for not writing +d on the left is incorrect. Still doesnt change the meaning and educational value of this lesson, and keep making videos! ❤

francaisdeuxbaguetteiii

Pay close attention to what's going on at 5:20; that's the secret to the entire problem. The Integrating Factor is applied so that the equation becomes an "exact" equation -- in other words, the left side of the equation becomes (xy)'.

In general, the Integrating factor satisfies the following requirement: what u(x) can you create such that u'(x) = u(x)*P(x)? Well, that would be u(x) = e^(integral of P(x)); when you differentiate it you get u'(x) = u(x)*P(x).

kingbeauregard

Could you do videos on 2nd order PDEs i.e homogenous and non-homogenous PDEs as well as the solution of the wave equation

peterchege

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