Question

Using the method of isoclines sketch the direction field for$$\mathbf{y}\mathbf{=}\mathbf{-}\frac{\mathbf{4}\mathbf{x}}{\mathbf{y}}$$.

Short answer

The graph is drawn below.

Step-by-step solution

The isoclines curve

Here the isoclines curve is

$$\begin{array}{c}\frac{\mathbf{-}\mathbf{4}\mathbf{x}}{\mathbf{y}}\mathbf{=}\mathbf{c}\\ \mathbf{y}\mathbf{=}\frac{\mathbf{-}\mathbf{4}\mathbf{x}}{\mathbf{c}}\end{array}$$

By putting the values of c we the graph.

By putting the different values of c=1,-1,2,-2 get the graph.

Slope field

By using the software we get the slope field.

By using the software and putting the different values of x get the slope field.

Direction field

By using the software get the direction field.

By using the software and putting the different value get the direction field.