Go to //www.examsolutions.net/maths-revision/index.php to see the main index of maths video tutorials and others on first order differential equations at ...
+Mace_In_Your_Face You can do it either way, people. Geeze. Is there only one way to solve any problem, is that what you're thinking? How the hell are you in DE courses if you havent figured it out yet that you can solve a problem however you want as long as the logic is sound.Try it either way. Or both ways.
Non-exact differential equation with integrating factor example
Check out //www.engineer4free.com for more free engineering tutorials and math lessons! Differential Equations Tutorial: Non-exact differential equation ...
It seems like all of differential equations could be covered in a week with
videos like this. I wish my professor would give videos instead of
lecturing. Our class notes are slightly less detailed than our textbook, so
we're basically rewriting the textbook on the board during lectures. I
don't understand it.
+Ben Swain Ah well at least my videos are helping a little! You can find the rest of the differential equations tutorials that I've made so far here: //www.engineer4free.com/differential-equations.html
Visit //ilectureonline.com for more math and science lectures! In this video I will review and solve the 1st order differential equation 3x^2-2y^2+(1-4xy)y'= 0 ...
How to solve non exact differential equations with an integrating factor
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No, there are many antiderivatives. An antiderivative of p(x) is a function
whose derivative is p(x), and there are infinitely many functions that will
do the trick. For example, if p(x) = 2x, then x^2 + C for any constant C is
an antiderivative. Now, it gets interesting when we try to figure out why
it doesn't matter which antiderivative we choose! After all, the
antiderivative appears in the formula at 1:36, wouldn't the formula change
if we choose a different antiderivative for p(x)?
Because every anti derivative of p(x) just differs by some 'const', so our
IFs will simply 'differ' by an 'e^const' - a constant factor. That factor
can therefore come out in front of the integral of 'r(x).q(x)' where it
will cancel with the constant factor in the '1/r(x)'
These two videos are the best explanations of the integrating factors
method that I've found, and I've watched everyone's videos. My mind is
blown; I'm definitely going to watch them again tomorrow and work through
them as you suggest.
When you say that we can use any antiderivative of p(x) that we choose for
the integrating factor, what do you mean? Isn't there only one
antiderivative for any given function?
Thanks for this. I'm in my first year of mechanical engineering, exams
coming up soon. This video series cleared up a lot of uncertainty I had
around ODEs