Example: How to Make and Interpret a Basic Slope Field

  1. Sketch the slope field for the differential equation y'=2y.
  2. Sketch the graph of the solution of y'=2y satisfying y(0)=1.
  3. What do we call the graph of a solution to a differential equation?

Answer:

We refer to the graph of a solution to a differential equation as an integral curve.

Slope Field for the Differential Equation y'=2y Slope Field for y'=2y with Solution Satisfying y(0)=1
Icon for Higher Math Notes: Differential Equations (A Higher Math Help Resource)

Video Explanation

Previous Note
Next Note

Navigation Tips:

  • To jump to a different lesson, use the navigation at the top of the page.

  • To cycle through the notes in the current lesson, use the Previous Note/Next Note buttons.