Question

\((x+y)(dx-dy) = dx + dy\) what to do when equations are parallel to each other.

Answer 1

Have you tried distributing then seeing if exact?

Answer 2

yes. I tried exact method.but didn't work for me

Answer 3

after re arranging it. I get\[\frac{dy}{dx} = \frac{x+y-1}{x+y+1}\]

Answer 4

\[(x+y)(dx-dy) = dx + dy\]\[xdx+ydx -xdy-ydy = dx + dy\]
\[(x+y-1)dx -(x+y+1) dy=0

Answer 5

\[(x+y-1)dx -(x+y+1) dy=0\]**

Answer 6

yeah. exact doesn't work. right?

Answer 7

It is one of these http://mathworld.wolfram.com/dAlembertsEquation.html

Answer 8

if it is not exact, you may try making it exact

Answer 9

and x+y-1 and x+y+1 are parallel. so solutions doesn't exist too

Answer 10

@ganeshie8 what do yo mean?

Answer 11

Did you check out the link? You should be able to get it from there. We can find another way if you haven't learned that yet.

Answer 12

give me a sec. I will read it

Answer 13

seems confusing. can you explain it.

Answer 14

make it separable with the sub v=x+y

Answer 15

@freckles seems working. wait a minute

Answer 16

go with freckles, then you don't need PDE

Answer 17

@freckles thanks. It worked

Answer 18

@FibonacciChick666 thanks for helping

Answer 19

sorry I wasn't better help. I always forget about substitution

Answer 20

\[v = y + x \\ y = v -x \\ \frac{dy}{dx} = \frac{dv}{dx} - 1 \ \rightarrow 1\]

Answer 21

\( \frac{dy}{dx} = \frac{x+v-x-1}{x+v-x+1} = \frac{v-1}{v+1}\)

Answer 22

\[\frac{dv}{dx} = \frac{2v}{v+1} \\ \int \frac{v+1}{2v}dv = \int dx\]

Answer 23

\[\frac{1}{2}v + \frac{1}{2}lnv = x + C \\ \frac{(x+y) + ln(y+x)}{2} = x + C\]

Answer 24

is that right?

Answer 25

I'd solve this one for C, but that is what I got

Answer 26

looks good

Answer 27

Thanks guys. I was struggling on this more than 1 hour. haha..

Answer 28

i didn't know a sub would work
it just look like it might once you put it in that one form you did the
y'=(x+y-1)/(x+y+1) form

Answer 29

that's the cool thing about math
you don't know what will work
and sometimes you have to just try things

Answer 30

no. @ganeshie8 also said about it before. but he didn't continue sub method. It perfectly worked..

Answer 31

exactly