Mathematics 162                   Laboratory 4 Homework                   Week of Feb. 15, 1993
	  
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© Lafayette College, 1994.

Part 0:  Drawing a Direction Field

This part of the lab project is to be done before you arrive in the lab.

Direction fields provide a graphical method for constructing solutions of differential equations.  The differential equation y' = f(x, y) says that the slope of the solution through the point (x, y) is the value f(x, y).  We indicate this on a graph by drawing a short line segment of slope f(x, y) through the point (x, y).  The collection of these line segments is called the direction field of the equation.

In preparation for laboratory, draw a portion of the direction field of the differential equation y' = x + y.  In this problem, f(x, y) = x + y.  Below is a table of values of f(x, y) for some representative points in the plane.  Use these values to draw a portion of the direction field in the plot below.  The line segments belonging to points whose coordinates are odd multiples of 1/2 are shown.  When you have completed filling in all sixteen line segments, try to draw in the solution to the differential equation that passes through the point (0, 1).  Remember that, at each point it passes through, the solution must remain tangent to the line segment of the direction field!  Make sure the curve extends in both directions from (0, 1).