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: Separate Variables Differential Eq. of Cubic Power

  1. Jun 4, 2013 #1
    1. The problem statement, all variables and given/known data
    When possible express the general solution in explicit form.
    Solve dy/dx =x^2 /(1+y^2)

    2. Relevant equations
    This is a first order non-linear ordinary differential equation.

    3. The attempt at a solution
    dy(1+y^2) = x^2 dx
    Integration both sides returns:
    y+ (y^3 )/3= (x^3)/3 +C
    Now, I am aware that there is more than one solution for y involving imaginary numbers. Can someone help me in the next step or direct me to a site?
    I have seen cubic solutions tutorial, but they involve equations of the form: Ax^3+Bx^2+Cx+D=0

    Thank you.
  2. jcsd
  3. Jun 4, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    I really don't think you want to solve for y. With an expression like that I'd just leave in the implicit form you already have, or maybe express x as a function of y instead. Don't try to use the cubic formula. It's a mess.
    Last edited: Jun 4, 2013
  4. Jun 4, 2013 #3
    Yes, I am aware that it is kinda difficult to solve for 'y' and that's why I wanted to try it out. It involves imaginary numbers and many roots.
    If someone can point me in the right direction, that would great.
  5. Jun 4, 2013 #4
    Luckily, this is a seperable equation, which means you can rewrite it as
    $$(1+y^2)dy = x^2dx.$$
    Now, what can you do to get rid of those pesky differentials?
  6. Jun 4, 2013 #5


    User Avatar
    Science Advisor
    Homework Helper

  7. Jun 4, 2013 #6
    Thank you, tiny-tim. I usually use latex for big equations, but I thought it wouldn't be a big deal.

    I was thinking that I could solve it like your wikipedia link... this will be interesting. Thanks.
  8. Jun 4, 2013 #7


    Staff: Mentor

    You really need to read through the thread. The OP has already done this and has gotten a solution.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted