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Homework Help: Solving a first order d.e

  1. Jul 10, 2008 #1
    1. The problem statement, all variables and given/known data

    For the d.e

    y' = x^2+y^2

    Show that the solution with y(0)=0 has a vertical asymptote at some point x_0,
    Then I have to try and find the upper and lower bounds for x_0

    I'm not able to solve this for y because when I bring the y^2 to the LHS

    3. The attempt at a solution

    I'm trying to learn differential equations on my own though readings and I'm having trouble getting the hang of it... for the above question I tried a few things such as

    y' - y^2 = x^2

    I've tried a number of methods including multiplying throughout by x and I can't
    find an equation whose differential is y' - y^2 OR xy' - y^2 because of the
    negative sign? SO my main prob is I can't begin to solve it for y(0)=0 because I
    don't know how to find y? Any help will be much appreciated!
  2. jcsd
  3. Jul 10, 2008 #2


    User Avatar
    Homework Helper

    This looks like a Riccati differential equation.
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