Question

directional fields

Answer 1

im unsure about 3 and 4, but i think eqn 5 is the graph from the bottom left corner and 6 at the upper right corner, isit correct?

Answer 2

put y' = 0 and see ... where slope is equal to zero for what

Answer 3

okay got it (:, so eqn 3, shd be lower bottom left? y=2 when y'=0,

Answer 4

okay im not sure of the rest :(

Answer 5

hold on a sec ,,, there are two values for y=2

Answer 6

what do u mean? at bottom left, it loks like its asymptote at y=2

Answer 7

at the top ... there is also a graph with y=0 as asymptote.
my guess is 4->left bottom, 3 -> top left

Answer 8

why is that?

Answer 9

just plot the family of curves,
k = x(y-2)

Answer 10

its not y'=0 also?

Answer 11

no ... you need to plot for whole different values ..

Answer 12

oh my like what are the starting values? how to find them?

Answer 13

you can put any value of slope ... y' = any value

Answer 14

okay i dont really get it ): shd we integrate it instead to get the function? idk if thts correct :p

Answer 15

integrating you get integral curves ... also probably you shouldn't integrate.

Answer 16

http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-i-first-order-differential-equations/geometric-methods/MIT18_03SCF11_s2_1text.pdf

Answer 17

okay! ill try what u said then haha

Answer 18

thanks!

Answer 19

3: left bottom (along x axis, the slope remains invariant)
4: left top (along x(y-2) = k, slope remains invariant)