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!

Homework Help: Using substitution in differential eq

  1. Aug 15, 2010 #1
    xdy/dx+y=1/y^2:using substitution in differential eq

    1. The problem statement, all variables and given/known data
    solve using substitution

    3. The attempt at a solution
    Thanks to the people who've help me thus far. here's a bernulli problem that I'm having. I change this problem around to...

    using u sub.

    substituted problem


    then I get e^(integral -3x)=e^(-3x^2/2)

    Here's where I'm stuck

    e^(-3x^2/2)u=integral 0*e^(-3x^2/2)

    doesn't that just have c? which later becomes
    However, that's not the solution of the equation which is

    Can someone explain why?
    Last edited: Aug 15, 2010
  2. jcsd
  3. Aug 15, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    There are three terms in your original DE, so you have dropped one. Also you need to be careful whether your x is in the numerator or denominator as you work. Use parentheses when there is doubt. After your substitution your DE should look like this:

    [tex]\frac 1 3 x u' + u = 1[/tex]

    Once you put that in correct form and find the integrating factor, you shouldn't have any ex terms.
  4. Aug 16, 2010 #3


    User Avatar
    Homework Helper

    And what about substituting u=xy?

  5. Aug 16, 2010 #4


    Staff: Mentor

    The DE is separable, which is something you should check for at the start in problems like this.

    The original equation is equivalent to
    [tex]\frac{y^2 dy}{1 - y^3} = \frac{dx}{x}[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook