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: Solving Bernoulli's Differential Equation

  1. Oct 5, 2016 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    integrating factor : u(x)=e∫p(x)dx
    standard form of linear DE: dy/dx + P(x)y=Q(x)
    standard form of bernoulli's differential equation: dy/dx + P(x)y=Q(x)yn
    change of variables v=y1-n
    3. The attempt at a solution
    xy(dy/dx)=y2 +x
    dy/dx=y/x +1/y


    multipliying both sides by y1 yeilds:
    y1(dy/dx) -y2/x=1

    using change of variable v=y1-n=y2
    and subbing the results yeilds:

    using an integrating factor to solve the resulting linear differential equation

    multiplying both sides of the equation by the integrating factor yeilds:

    integrating both sides:
    (1/2)v/x=ln|x| + C
    v=2ln|x| +C

    now subbing back in y2]
    y2]=2ln|x| + C

    Unfortunately the answer is :


    where did I go wrong?
    Thanks ahead of time, you guys rock
  2. jcsd
  3. Oct 5, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Your equation is not in the proper form for the integrating factor. The leading coefficient must be ##1##, so you need to multiply your equation by ##2## before continuing.
  4. Oct 6, 2016 #3
    thanks a bunch, I got it now
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted