1. Not finding help here? Sign up for a free 30min 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!

Stuck in solving a (rather simple) differential equation problem.

  1. May 6, 2009 #1
    1. The problem statement, all variables and given/known data
    Equation: dy/dx=x+1/3y^2 where y>0


    2. Relevant equations
    I'm to show that (1/2x^2+x+8)^1/3 is a solution


    3. The attempt at a solution
    Splitting it up in x/3y^2+1/3y^2 has been futile and I'm out of ideas.

    Can anyone help me see the light?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 6, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Is this 1+ (1/3)y^2 or 1+ 1/(3y^2) or (x+ 1)/(3y^2)?


    So you are NOT required to solve the equation? If y= ((1/2)x^2+ x+ 8)^(1/3), what is y'? Of course, y^2= ((1/2)x^3+ x+ 8)^(2/3). Put those into the equation and show that the the equation is satisfied.


     
  4. May 6, 2009 #3

    epenguin

    User Avatar
    Homework Helper
    Gold Member

    Yes, like many other problems in math, it is easier to solve a differential equation when you know the solution.

    That may seem like cheating, but actually a rather well kept secret is that the only way to solve a differential equation is to know the solution, at least in outline.

    Perhaps this concept can be further generalised. :shy:
     
  5. May 6, 2009 #4
    Thanks HallsofIvy, you saved my day.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook