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Differential Equation - Where am I going wrong?

  1. Sep 22, 2013 #1
    1. The problem statement, all variables and given/known data

    Using Euler's Method:

    a) Find the approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0.3, and 0.4 using the Euler method with h= 0.1

    b) Repeat part (a) with h = 0.05.

    I am doing part (b). The function is y' = 0.5 - t + 2y, y(0)=1


    2. Relevant equations
    For Euler's Method:
    y_n = y_n-1 + h * F(x_n-1, y_n-1)

    3. The attempt at a solution

    I've done it according to the book, using Euler's Method. I am trying to find y_1 but am not coming up with the book answer, for (b).

    h = 0.05
    so t = 0.05, 0.10, 0.15, 0.20 (but not interested in these yet, just want y_1 to be right!)


    y_1 = 1 + (0.05) [0.5 - 0 + (2)(1)]
    should be 1.26, but I get the wrong answer. What am I doing wrong? :(

    Thanks
     
  2. jcsd
  3. Sep 22, 2013 #2

    Office_Shredder

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    Gold Member

    I think you have the correct formula for y1. I will observe that y2, which is your approximation for y(.1), is in fact 1.26 if you take the next step. You are simply confusing what you're supposed to be comparing to your answer sheet.
     
  4. Sep 22, 2013 #3
    Thank you!!
     
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