Question

Use separation of variables to solve the differential equation dy/dx = 1+x/xy with initial condition y(1) = -2

(Hint: After you isolate 1+x/x on one side of the equation, break it into the sum of two fractions.) You get the solution:

(see attachment)

Answer 1

\[\frac{dy}{dx}=\frac{1+x}{xy}\]
Since you have asked a question like this earlier
Do you want to tell me how you would separate the variables?
I can tell you if you are wrong or right.

Answer 2

multiply dx on both sides and dy on both sides right?

Answer 3

1) Multiply dx on both sides is right
2) multiply both sides by y ( not dy )

So we would have
\[y dy =\frac{1+x}{x} dx\]
right?

Answer 4

lol

Answer 5

@shubhamk It is against the CoC to give just answers. Thanks.
Please read the CoC http://openstudy.com/code-of-conduct

Answer 6

So now we want to integrate both sides

Answer 7

I thought the Y would cancel dy

Answer 8

wait a moment then

Answer 9

which is y^2/2 = something

Answer 10

\[y dy =(\frac{1}{x}+\frac{x}{x}) dx\]
\[y dy=(\frac{1}{x}+1) dx\]

no y doesn't cancel dy


So integrate both sides :)

Answer 11

Yes that side is right
good job

Answer 12

wait

Answer 13

yes?

Answer 14

can i flip 1/x and make it -x/1?

Answer 15

no
1/x=x^(-1)

but
anti-derivative of 1/x is ln|x| right?

Answer 16

I dont know your gonna have to do this one and explain.

Answer 17

just integrate it simply to obtain ln|x| + x + C(constant of integration) = (y^2)/2
can u do till here, she explined a lot

Answer 18

??

Answer 19

you gave me the answer anyway. thanks!

Answer 20

and thanks for explaining!

Answer 21

i gotta see this code of conduct then

Answer 22

I didn't even know about it.

Answer 23

hey, can try my question???

Answer 24

http://openstudy.com/study#/updates/4f988af8e4b000ae9ece2c33