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Find the general solution to the differential equation

  1. Jun 15, 2012 #1
    Find the general solution to the differential equation
    y'+(12x^11)y=x^12

    Use the variable I= the integral of e^(x^12)dx where it occurs in your answer.

    According to some people, it doesn't have an elementary solution, look at:
    http://www.wolframalpha.com/input/?i=y%27+%2B+12*x^11*y+%3D+x^12

    there's a incomplete gamma function ?

    can someone please show me how to solve this problem, thank you so much!
     
  2. jcsd
  3. Jun 15, 2012 #2
    Hi ani9890! Welcome to PF :smile:

    Wolfram Alpha has a strange way of solving differential equations. But there is an elementary solution, as it is a simple linear differential equation. How can you solve such equations?

    Hint : Start by analyzing what the integrating factor is...
     
  4. Jun 15, 2012 #3
    so I end up with this,

    d/dx[ye^(x^12)] = x^12*e^(x^12)

    and I'm supposed to integrate both sides, but the right side can't be integrated to give a elementary solution. So what should I do?

    I was thinking y(x)=e^(-x^12)(x^12)I
    where I stands for the integral of e^(x^12) , but I'm sure this is wrong lol
     
  5. Jun 15, 2012 #4

    SammyS

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    No:

    [itex]\displaystyle \frac{d}{dx}\left(ye^{\displaystyle x^{12}}\right)=y'\ e^{\displaystyle x^{12}}+y\,e^{\displaystyle x^{12}}\left(12x^{11}\right)[/itex]

    So, what if you multiply your Dif.Eq. by e12x ?
     
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