Question

Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each of the indicated points.

dy/dx = 1 − xy
(a) y(0) = 0
(b) y(−1) = 0
(c) y(2) = 2
(d) y(0) = −4

Answer 1

Answer:

Answer curve attached as a picture.

Step-by-step explanation:

Let us first find derivatives using the given function at the given points.

GIVEN FUNCTION:

$\frac{dy}{dx} = 1 - xy$

At P(0,0);

$\frac{dy}{dx} = 1 - (0)(0)$

$\frac{dy}{dx} = 1$

At P(-1,0);

$\frac{dy}{dx} = 1 - (-1)(0)$

$\frac{dy}{dx} = 1$

At P(2,2);

$\frac{dy}{dx} = 1 - (2)(2)\\\frac{dy}{dx} = 1 - 4\\\frac{dy}{dx} = -3$

At P(0,-4)

$\frac{dy}{dx} = 1-(0)(-4)\\\frac{dy}{dx} = 1-0\\\frac{dy}{dx} =1$

To plot the solution curves for each point, we first use the derivatives of these points and draw them on these points as the initial slope of the corresponding curves. Then we join them with the corresponding slopes of direction field.

I have generated the direction field using online open source website by inputting the given function.