9.2 Differential Equations
Direction Fields & Euler’s Method
Question #1 (Medium): Sketching the Direction Field for Differential Equation
Differential equation for a given combination of and , the slope at that coordinate is equal to
which is given by the differential equation. You can keep track of these coordinates along with the
slope at the point, or take some sample values for the slope and work out the equation backward for
and relationship that produces that slope anywhere. Then for connect these short slope lines at a
given point as a sketch representing the solution curve passing through that point.
Sketch a direction field for the differential equation. Then use it to sketch three solution curves.
The given differential equation is affected only by the y variable and not . First draw the and axis,
and lay out the grid lines focusing on the values that affect the slope.