Results 1 to 3 of 3

Math Help - First order, homogenous DE

  1. #1
    Member
    Joined
    Jan 2011
    Posts
    88

    First order, homogenous DE

    Find the values a and b such that the positive function y(x) defined implicitly by the equation x^a=Ae^{-(xy)^b} satisfies dy/dx+y/x=(5/4)x^3y^5. Note: y(1)=2

    Looking for a hint as to how I should tackle this problem. I implicitly differentiated the first equation and ended up with dy/dx+y/x=(-ax^{a-2})/(Ab(xy)^{b-1}). I really don't know though. I am stumped.
    Last edited by quantoembryo; February 26th 2013 at 12:01 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2011
    Posts
    245
    Thanks
    56

    Re: First order, homogenous DE

    Implicit differentiation of the first equation leads to dy/dx which has to be brought back into the ODE.
    So, you must not have dy/dx remaining after simplification and the equation becomes very simple. Then, a and b are straightforwards obtained.
    Probably, there is a mistake somewhere in your calculus. But without seeing the details of your calculus it is impossible to show you where is the mistake.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2011
    Posts
    88

    Re: First order, homogenous DE

    I will hit the drawing boards. Thanks!

    Edit: I ended up getting the correct results! Thanks!
    Last edited by quantoembryo; February 27th 2013 at 07:43 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving second order non-homogenous DE
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: April 21st 2011, 05:59 AM
  2. Second Order DE (non homogenous)
    Posted in the Differential Equations Forum
    Replies: 8
    Last Post: August 13th 2010, 01:12 PM
  3. second order non-homogenous IVP
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: July 23rd 2009, 05:44 AM
  4. Third Order Non-Homogenous ODE
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: June 25th 2009, 04:08 AM
  5. Replies: 1
    Last Post: May 11th 2007, 03:01 AM

Search Tags


/mathhelpforum @mathhelpforum