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Homework Help: Simple differential eq'n problem, check my answer please!

  1. Sep 20, 2013 #1
    1. The problem statement, all variables and given/known data

    dy/dt=2y+3, y(0)=0.06, find y(1)= ?, Δt=0.1

    2. Relevant equations

    y_k+1 = y_k + Δt*f(t_k, y_k)

    3. The attempt at a solution

    y_1 = y_0 + Δt*f(t_0, y_0)
    y_1 = 0.06 + 0.1*(2(0.06)+3)=0.372

    y(1) = 0.372??
    this doesn't seem right because I did this on excel and i got around a y(1)~4.00. the margin of error seems way to big. help!!
  2. jcsd
  3. Sep 20, 2013 #2


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    Homework Helper

    You did the first step of iteration only, and calculated y(0.1). Repeat it nine more times. (But it will be a very poor approximation of y(1).)

  4. Sep 20, 2013 #3

    is there any way of solving y(1) without doing it nine more times? because my next hw problems has step size 0.01...
  5. Sep 21, 2013 #4

    D H

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    Staff Emeritus
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    Use a spreadsheet.
  6. Sep 21, 2013 #5
    my teacher wants me to compare my approx value with my the spreadsheet value. I was wondering if there was a fast shortcut to calculate by hand y(1) with step sizes like 0.1 or .01? or is the only way to do it is one by one until i reach value y(1)?
  7. Sep 21, 2013 #6


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    It is easy to solve the differential equation by an exact way. If you consider y as the independent variable, dt/dy = 1/(2y+3). If the derivative of a function f(y) is 1/(2y+3), what is the function?

    t=(1/2) ln|2y+3| + C, y= Ae2t -1.5, with the initial condition, y=1.56e2t -1.5

  8. Sep 21, 2013 #7
    oooh i actually did do that but I thought I was wrong because my approx value was y(1)=10.0269, which is way different from the excel value of ~4.00. are the error margins usually this big?
  9. Sep 21, 2013 #8
    what did you make that A variable equal to?
  10. Sep 21, 2013 #9


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    I got the same y(1) ≈10. The simple iterative method you applied is quite poor, you have to use very small Δt-s to get near to the real solution. With Δt=0.01 it would be much better. But there are more advanced methods for numerical solution of differential equations, Runge-Kutta method, for example. All of them involve lot of computations, so you need a program to do them.

    Last edited: Sep 21, 2013
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