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: Solve For Exact Differential Equation

  1. Jan 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve the exact equation y^3-(14x+2)dx+3xy^2dy=0

    2. Relevant equations


    3. The attempt at a solution

    I proved these were exact because dM/dy and DN/dx both equal 3y^2

    I chose to work with N first and df/dy=3xy^2

    Therefore f(x,y)=xy^3+h(x)

    I took df/dx of this and got y^3 + h'(x)

    I made this equal to the other df/dx so it looks like:
    df/dx = y^3+h'(x)=y^3-(14x+2)

    h'(x)=-14x+2 and so h(x) is -7x^2+2x (+ constant)

    I plugged this into the original problem with h(x) so it now looks like:


    Solving for y, I get y=(-7x^2+2x+C)^(1/3) / x^(1/3)

    This is not correct and I don't know what I'm missing here.
  2. jcsd
  3. Jan 31, 2012 #2


    User Avatar
    Science Advisor

    You have a basic algebra error! -(14x+ 2)= -14x- 2, not -14x+ 2.
  4. Jan 31, 2012 #3
    Ah yes. I did it again from the beginning and was able to solve it correctly. Thanks for pointing out the error. :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook