Question

The family of curves represented on this graph would appear to be consistent with which of the following differential equations?

Answer 1

dy/y/x
dy/dx = tan(x+y)
dy/dx = xsqrt(x-3)
dy/dx = 3x^2
dy/dx=x+y

Answer 2

@phi

Answer 3

what does the first line dy/y/x mean ?

Answer 4

sorry the first possible answers is:
dy/dx = y/x

Answer 5

dy/dx = y/x
means at the points where y=x (the diagonal from (0,0) to (1,1), extended.
the slope should be 1 i.e. 45 degrees.
notice that near (2,2) the little "lines" are pointing mostly up. definitely not slope 1
so rule out the first choice.

Answer 6

for
dy/dx = 3x^2
this says the slope is independent of y. i.e. at a particular x, if we move up or down, the slope of the little lines should remain the same.
for example, look at x=0. as we move up the y-axis, the "little lines" are changing slope.
that means we can rule out this choice.

Answer 7

for
dy/dx = xsqrt(x-3)

here again, the slope is independent of y (should not change as we move up or down)
but as in the previous case, this is not true. so rule out this case.

Answer 8

you are left with either
dy/dx = tan(x+y)
dy/dx=x+y

Answer 9

Is it dy/dx = x+y?

Answer 10

@phi

Answer 11

check a few cases.
when x=0 and y=-1 the slope should be -1 (45 degrees down)

Answer 12

based on a few checks, x+y looks good.

Answer 13

tan(x+y) should show "spin" because x+y (interpreted as radians) will repeat modulo pi radians.

Answer 14

Thank you very much!