Question

A differential equation, a point, and a slope field are given.  (a) Sketch two approximate solutions of the differential equation on the slope field, one of which passes through the given point. (b) use integration to find the particular solution of the differential equation and use a graphing utility to graph the solution. Compare the result with the sketches in part (a). To print an enlarged copy of the graph, go to the website www . mathgraphs . com.

Answer 1

Step 1:

(b) The differential equation is and the point is .

.

Integrate on each side.

Substitute the point in above solution to find the value.

Substitute in solution function.

.

Graph:

Graph the solution function.

Solution:

(b)

 

Answer 2

Step 1:

(a) The differential equation is and the point is .

Solution of the differential equation is .

One solution at the point is .

Consider to graph another approximate solution.

Second approximate solution is .

Graph:

Graph the differential equation .

Graph the two approximate solution to the differential equation.

Solution:

(a)