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: Need help solving a differential equation

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data

    xy' - (x+1)y = 0, y(0) = 5

    2. Relevant equations

    Well all of the differential equation stuff seems relevant to me. But from the beginning dy/dx + P(x)y = Q(x) and yeintegral(P(x)dx) = integral(Q(x)eintegral(P(x)dx)dx + C. The separation of variables M(x)dx + N(y)dy = 0.

    3. The attempt at a solution

    Well I tried following separating everything out: xy' - (x+1)y = 0 y' - ((x+1)/x)y = 0/x then p(x) = -(x+1)/x and eintegral(P(x)dx) = e-integral((x+1)/x dx) and using some more math we end up with e-x/x and that is where I fall apart. Do I integrate this new function and then what? I come up with x/e-x for y and (x-1)ex for y' but when I put it back into the original equation i get x2 + x = x2 -x. Where did I go wrong?
  2. jcsd
  3. Apr 26, 2009 #2
    Be careful...you're dividing by x but the initial condition is for x=0. You need to consider the function on an open interval about x=0 and so you cannot divide by x.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook