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)

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)

amistre64 · Answer

might need alittle more context

amistre64 · Answer

what did 4 look like to begin with?

anonymous · Answer

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

amistre64 · Answer

ahh, integrating factor

anonymous · Answer

yep,i didn't get that step

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

yeah

anonymous · Answer

oh right
thanks :D

amistre64 · Answer

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

anonymous · Answer

thanks man :)

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

good luck ;)