The diffrential equation is .

The general solution is .

The particular solutions of  are .

Draw the graphs for different values of .

(1). Draw the coordinate plane.

(2). Graph the function .

Graph :

Observe the graph :

The graph obtained when  is two intersecting lines.

(1). Draw the coordinate plane.

(2). Graph the function .

Graph :

Observe the graph :

The graph obtained when  is a hyperbola.

(1). Draw the coordinate plane.

(2). Graph the function .

Graph :

Observe the graph :

The graph obtained when  is a hyperbola.

(1). Draw the Coordinate plane.

(2). Graph the function .

Graph :

Observe the graph :

The graph obtained when  is a hyperbola.

(1). Draw the Coordinate plane.

(2). Graph the function .

Graph :

Observe the graph :

The graph obtained when  is a hyperbola.

Particular solutions :

When , the garph two intersecting lines.

When , the graph is a hyperbola.

When , the graph is a hyperbola.