Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding slope fields using Euler method

  1. Jun 2, 2010 #1
    hi guys,

    can someone give me a quick tutorial on how to solve and explain to me the concept of slope field of the following differential equation:
    sketch the slope field for dy/dt = 2t+1
    showing the solution y=t^2+t-4, which satisfies the initial condition y(-2)= -2

    Also how to use the Euler's method to solve the slope field of the above differential condition.

  2. jcsd
  3. Jun 2, 2010 #2


    User Avatar
    Science Advisor

    Choose a number of points in a ty- coordinate system (t is the horizontal axis, y the vertical axis. At each (t, y) point, draw a short line segment having slope 2t+ 1. Since that does not depend on y, you can do that by marking lines with the same slope in a vertical "stack".

    Now, starting at the point (-2, -2), draw a curve that is always tangent to those line (use the short lines to give the direction at each point). The curve should look like [itex]y= t^2+ t- 4.

    You don't use Euler's method to "solve the slope field". Euler's method is used to find a numerical approximation to the solution to a differential equation problem.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook