1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to get started on this?

  1. Apr 14, 2005 #1
    Q. If dy/dx = e^x / x and y(1) = 2; find an approximate value for y(3). Use a technique from calculus or technology to help you solve the problem. It is impossible to find an antiderivative.

    My thoughts / ideas:

    I thought this was a separable equation, and could separate the x and y variables and then may be just integrate both sides.

    But I don't think this is possible, Since the question clearly says "It is impossible to find an antiderivative".

    Any ideas.
  2. jcsd
  3. Apr 14, 2005 #2
    Linear approximations? Eulers method?
  4. Apr 14, 2005 #3
    Yeah, I think you are right, Euler's Method would work definetly.

    How about using calculus. any ideas.

    I can make a 'spreadsheet' in Excel that can calculate the differential at the specified point

    using Euler's Method and Euler's Improved method.

    But any ideas on how to actually use calculus.
  5. Apr 14, 2005 #4
    Euler's method and linear approximations are calculus methods.
  6. Apr 14, 2005 #5
    I used the fact that delta(y) is roughly equal to delta(x) times dy/dx. Then you come up with y(3)-y(1)=(e^1/1)(3-1). I think this gives y(3)= 2e+2. Could someone verify that this is the correct approximation?

    Thanks, Joe
  7. Apr 14, 2005 #6
    Ok, Let us give up technology for a moment ,and actually think , how to solve this problem analytically using calculus.

    I know we could use Euler's Method or Linear Approximation, but how do we apply them analytically .. How to get started?

    Please help!
  8. Apr 14, 2005 #7
    1)I think that you can make fast work on this question by using McClaurin's expansion for e^x, then divide it later by x to find dy/dx (in a summation notation for easy integration later)
    2) For the second part, since the initial value is given we can use the fundamental theorem of calculus to find a short cut to the general form of the solution.
    (i.e) [tex]y=\int_{1}^{x} f(t)dt +2 [/tex]

    f(t) here is simply the series expansion for [tex]e^x/x[/tex]
  9. Apr 14, 2005 #8


    User Avatar
    Science Advisor
    Homework Helper

    I resent that and claim it's incorrect,because

    [tex] \int \frac{e^{x}}{x} \ dx =\mbox{Ei}\left(x\right) +C [/tex]

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: How to get started on this?
  1. Trouble getting started (Replies: 15)

  2. Force of sneeze (Replies: 6)