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: Use u = y' substitution to solve (y + 1) y'' = (y')^2

  1. Mar 11, 2014 #1


    User Avatar

    1. The problem statement, all variables and given/known data
    Solve the following differential equation, by using the substitution u = y'.:
    (y + 1) y'' = (y')^2

    2. Relevant equations
    I'm assuming: Chain Rule

    3. The attempt at a solution
    My problem is, simply, that I don't get how to go from u = y' to y'' = u du/dy, and I would appreciate it if someone could show me how!

    Other than that, I should be fine.
  2. jcsd
  3. Mar 11, 2014 #2


    User Avatar
    Gold Member


    (y+1) u' = u²

    then rearrange to get u's on the left and y's on the right and integrate.
    (this is a classical manipulation in classical mechanics)
  4. Mar 11, 2014 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I will use prime for differentiation with respect to the independent variable which I will assume to be ##x##. We have the substitution ##u(y) = y'##. Differentiating both sides with respect to ##x## gives$$
    y'' = u'(y) = \frac{du}{dy}\cdot y' = u \frac{du}{dy}$$It's just the chain rule and I switched the factors in the last step.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted