Results 1 to 2 of 2

Thread: finding a singular solution

  1. #1
    Oct 2009

    finding a singular solution

    I am having trouble with this problem. I believe that there is a singular solution involved in it yet I do not know how to find it.


    so far i have rewritten the problem as
    (z'')(z^2)-(z')^3=0 , made the substitution u=z' and continued to solve that using separation of variables. I still do not understand how to find the singular solution though

    thank you for any help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Aug 2008
    How about we write it as just $\displaystyle y'' y^2=(y')^3$

    By inspection you can see $\displaystyle y=k$ is a solution including the solution $\displaystyle y=0$ right? So letting $\displaystyle y'=p$ and making that substitution, I get $\displaystyle pp'y^2=p^3$ and I can do the division to obtain $\displaystyle \frac{dp}{dy}p^{-2}=y^{-2}$ only if $\displaystyle p\neq 0$ and $\displaystyle y\neq 0$. Doing that, and integrating twice, I obtain the solution:

    $\displaystyle c_1 y+\ln(y)=x+c_2$. Now note that the solutions $\displaystyle y(x)=k$ are not particular cases of this solution and it looks like the general solutions are asymptotically tangent to the solution $\displaystyle y=0$ but not the other y=k solutions. I'm a little unsure about this part as to whether all the y=k solutions are singular or just the y=0 one.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Feb 10th 2011, 04:57 PM
  2. To show a solution becomes singular
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: May 13th 2010, 01:40 AM
  3. Finding singular points of a curve in affine space
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Mar 29th 2010, 03:35 AM
  4. Finding the general solution from a given particular solution.
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: Oct 7th 2009, 01:44 AM
  5. Replies: 8
    Last Post: Jul 9th 2008, 12:09 PM

Search Tags

/mathhelpforum @mathhelpforum