Visual representation of solutions to a differential equation
The slope field of , with the blue, red, and turquoise lines being , , and , respectively.
A slope field (also called a direction field[1]) is a graphical representation of the solutions to a first-order differential equation[2] of a scalar function. Solutions to a slope field are functions drawn as solid curves. A slope field shows the slope of a differential equation at certain vertical and horizontal intervals on the x-y plane, and can be used to determine the approximate tangent slope at a point on a curve, where the curve is some solution to the differential equation.
^Boyce, William (2001). Elementary differential equations and boundary value problems (7 ed.). Wiley. p. 3. ISBN 9780471319993.
^Vladimir A. Dobrushkin (2014). Applied Differential Equations: The Primary Course. CRC Press. p. 13. ISBN 978-1-4987-2835-5.
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