1. Limited time only! Sign up for a free 30min personal 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!

Integration by Parts/Differential Equation

  1. Sep 27, 2006 #1
    If you have [tex] \int e^{x^{2}}x^{2} [/tex] would it be reasonable to choose [tex] u = e^{x^{2}}, dv = x^{2}, du = 2xe^{x^{2}}, v = \frac{x^{3}}{3} [/tex]? And then I get [tex] x^{3}e^{x^{2}} - 2\int x^{4}e^{x^{2}} [/tex]. Would this be equivalent to choosing [tex] u = x, dv = 2xe^{x^{2}}, v = e^{x^{2}}, du = dx [/tex].

    This was for solving a differential equation:

    [tex] \frac{dy}{dx} + 2xy = x^{2} [/tex], where [tex] P(x) = 2x, Q(x) = x^{2}, I = e^{\int 2x} = e^{x^{2}} [/tex]. So [tex] (ye^{x^{2}})' = e^{x^{2}}x^{2} [/tex]

    [tex] y = e^{-x^{2}} \int e^{x^{2}}x^{2} dx + C [/tex]

    Last edited: Sep 27, 2006
  2. jcsd
  3. Sep 27, 2006 #2
    You should note that
    so that your integrand can be written as
    Then you can integrate this by parts.
    By the way in your expression for [itex]y[/itex] you seem to have lost the homogeneous solution.
    A further note is that you might find it useful to have a look at the error function when trying to evaluate your expression:


    (....and you shouldnt have the constant C in your expression for [itex]y[/itex], it should be attached to your homogeneous solution....)
    Last edited: Sep 27, 2006
  4. Sep 27, 2006 #3
    thank you for your help
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Integration Parts Differential Date
Integration by parts/substitution Nov 2, 2017
Solving an Integral Sep 23, 2017
Integration by parts and approximation by power series Sep 15, 2016
Separable differential equation and Integration by parts Dec 14, 2010