Question

in linear differential equations chapter
I didn't get this step
So we can replace the left side of (4) with this product rule. Upon doing this (4) becomes

(u(t)y(t))' = u(t)g(t)

Answer 1

might need alittle more context

Answer 2

what did 4 look like to begin with?

Answer 3

http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx
check step from step 3

Answer 4

ahh, integrating factor

Answer 5

yep,i didn't get that step

Answer 6

they are making the integrating factor very vague at the moment ... and ask you not to be concerned to much about what it is

Answer 7

but notice that the product rule for uy is simply: uy' + u'y

right?

Answer 8

yeah

Answer 9

oh right
thanks :D

Answer 10

so to recap:

if you have:

y' + py = g , lets multiply this by some u

uy' + upy = ug . lets also assume the upy = u'y

uy' + u'y = ug , since uy' + u'y = (uy)' we get

(uy)' = ug

Answer 11

thanks man :)

Answer 12

yep, towards the end theyll clear up this mystery of "u" ... it has to do with the properties of using "e" and its derivatives

Answer 13

oh I see.
wellm gonna clear 1st order DE today,so lets see :D

Answer 14

good luck ;)