The following direction field corresponds to which of the fo

The following direction field corresponds to which of the following differential equations? Select only ONE answer. y\' = sin (3 x) y\' = 3x / y y\' =3xy y\' = 3y

Solution

The problem can be solved only by checking the choices with the figure (and some intuition)
follow these steps :-

1)first we note that along x axis line is horizontal and the slope is zero. therefore when x =0, y\' = 0. Therefore fourth option is not possible

2)we note that the plot is symmetric along x axis. and it varies with the value of y. therefore the slope expression should depend on y.

3) we can see that when y tends to infinity, line becomes vertical i.e slope tends to infinity and when y tends to zero, slope tends to zero. therefore clearly the only option possible is the second one.

Therefore the answer is 3x/y