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: General rule regarding solving each differnetial

  1. Jan 30, 2010 #1
    1. The problem statement, all variables and given/known data

    (3y^2 + 2y)y' = xcosx
    xyy'=ln(x) ; y(1)=2

    2. Relevant equations

    3. The attempt at a solution
    for the first one i get y^3 + y^2= (x^2) sin(x) +cos(x) + C (constant)
    and the second one is y^2 + ln(x)^2 +4
    the problem is there is no way i can define those two as function y of x or function x of y
    because of the exponents.

    So my question is, if a question is asking for a solution to a differential equation, can we just leave it as that above?
  2. jcsd
  3. Jan 30, 2010 #2


    Staff: Mentor

    The left side is correct, but you made a mistake when you integrated xcos(x). You can check what you have by differentiating x2sin x + cos x. If your integration is correct, you should get d/dx(x2sin x + cos x) = xcosx.

    Once you fix your error, you're done. It's not always possible to get the solution so that you have y as a function of x. In this case you will have y as an implicit function of x.
    You might have made a typo here. The solution should be y2 = (ln x)2 + 4. It's probably OK to leave it this way, but if you need to, you can solve for y, as y(x) = +/-sqrt( (ln x)2 + 4)
  4. Jan 30, 2010 #3
    yeah i made a typo in both solutions. Im sorry. I was really rushed to type it in

    the first one should be y^3+y^2 = xsin(x) +cos(x) + C and the second one is y^2 = (ln x)^2 + 4 not y^2=ln(x)^2 +4
    Last edited: Jan 30, 2010
  5. Jan 30, 2010 #4


    Staff: Mentor

    Both look fine now.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook