[SPLIT] Solve xy' + y = 1 + y' for y'

[password]

I have one more quick question.. The directions are to "Solve for y' "

Here's the problem...

xy' + y = 1 + y'

Here's what i've done so far.. But then I got stuck..

xy' +y - y' = 1
xy'+y' = 1 - y
y' + y'/x = (1-y)/x
(y'x+y')/x = (1-y)/x

Any hints/suggestions would be greatly appreciated. Thanks

 

[stapel]

xy' + y = 1 + y'

Here's what i've done so far.. But then I got stuck..

xy' +y - y' = 1
xy'+y' = 1 - y
y' + y'/x = (1-y)/x . .<= I don't understand what you're doing here...? :shock:
(y'x+y')/x = (1-y)/x

Once you have the following:

. . . . .xy' + y' = 1 - y

...factor out the y'.

. . . . .y'(x + 1) = 1 - y

Now divide through by the parenthetical. :wink:

Hope that helps!

Eliz.

 

[scoresofsteel]

one tip will be that in such kind of questions : the term that has to solved for, should be kept together, so that at right time you can derive that term out as a common factor.

e.g. in this question term to be solved for is y'


so i might decide to keep all factors with y' on one side.

xy' and y' have "y'", lets bring them on left hand side and move others on right.

xy' - y' = 1 -y

now its easy to extract out y' as a factor on left hand.

y'(x - 1) = 1 - y

finally ...

y' = (1 - y)/ (x - 1)