9.2 Differential Equations
Direction Fields & Euler’s Method
Question #2 (Medium): Direction Field & Solution Curve Passing Through a Point
First consider drawing tangents with 0 slope. Then work with easy integers for ( ) like . Also
see what happens along the axis and axis. Then compare the quadrants for any symmetry with
negative and positive and combinations. Solution curve means at the assigned point, connect the
directional lines to get a solution curve.
Sketch the direction field of the differential equation. Then use it to sketch a solution curve that passes
through the given coordinate.
First start from 0 slope. When and are both , the slope is zero. Also wherever , the slope is
zero. From plane, at these points, draw short lines of flat line.
Also by setting the right side can be factor