Question

Which of the following differential equations is consistent with the following slope field?

Answer 1

@Kainui

Answer 2

Slope at the point (x,y) is the value of \(\frac{dy}{dx}\) which is a function of x and y so you can think of it as the function \(\frac{dy}{dx} (x,y)\). So look for stuff you know. What have you tried?

For instance, you know since the top is a reflection of the bottom then that means \[\frac{dy}{dx}(x,y) = \frac{dy}{dx}(x,-y)\]

Try plotting some points of the choices you're given, that can help too.

Answer 3

check one by one.
the first one x/y^2,
y^2 >0 for all y, right? hence dy/dx 's sign depend on x only. if x <0 ,then dy/dx <0
look at the quadrant 2 and 3 . At quadrant 2 , you have / line, that is slope >0, hence the first one is NOT the solution

Answer 4

the second one, x/y
dy/dx >0 if both x>0 and y>0 or x<0 and y<0
Quadrant 1 and 3 satisfy both x,y >0 or x,y<0, that is dy/dx at those quadrant must be / lines
but in quadrant 3, you have \ , that is slope <0 , hence 2 is NOT a solution also.

Answer 5

the last one is x^2/y^2 >0 for all x, y, but your graph has \ lines, so, the last one is NOT a solution also.
You can test the third one.

Answer 6

I got I had gotten third option as my answer. Thank you for you opinion too :)

Answer 7

ok

Answer 8

can you help me with another question?

Answer 9

Not sure, have to see it first

Answer 10

ok let me post it

Answer 11

I got B. Do you think that's right?

Answer 12

yup

Answer 13

you sure?

Answer 14

sure, I solve it by myself, not just look at your solution

Answer 15

okay just making sure. Thanks again :)

Answer 16

hehehe, fortunately, I am reviewing for my tomorrow final. I like practice on those problems like this.

Answer 17

r u taking calculus?

Answer 18

ODE

Answer 19

ODE?

Answer 20

yup, kind of calculus 4 or 5 hahaha....

Answer 21

oh okay haha. Well i'm gonna be on for a while and I could use the help. U mind if I tag you later maybe?

Answer 22

no problem, I have test tomorrow , and another one on Tuesday and I am done. I graduate. No more test, I am free.

Answer 23

And I don't want to lose what I earn. That is why I am here to practice every day on others' problems.

Answer 24

I guess we both will get practice. Well I ttyl then :) thanks again bye

Answer 25

bye