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Re-post Solution to DE

  1. Nov 6, 2014 #1
    1. The problem statement, all variables and given/known data
    Solve DE: y' -2 y / (x + a) = -1 where a = constant

    2. Relevant equations
    y' + p(x) y = q(x) solving this DE with integrating factor.

    3. The attempt at a solution
    Use integrating factor (x+a) ^ -2 for above DE,

    [ y'(x+a) ^ -2 ]' = - (x+a)^ -2 solving this DE we get

    y = C(x+a)^2 + (x+a) this seems to be a solution, C = arbitrary constant

    Is this the only solution??
     
  2. jcsd
  3. Nov 6, 2014 #2
    Yes, your 1-parameter family of solutions contains every particular solution. In fact, every equation of this form, when solved by multiplying by the integrating factor of the exponential of the integral of p, will yield a 1-parameter family of solutions that contains every particular solution, as long as p and q are continuous on the interval of the solution.
     
  4. Nov 6, 2014 #3

    Mark44

    Staff: Mentor

    The above isn't right. The left side is [y * (x + a)-2]', or in another form d/dx[y * (x + a)-2].
     
  5. Nov 6, 2014 #4
    (x+a)^-2 = (x+a) elevated to the -2 power (I am not used to this sites equation editor)

    Thanks for your reply,
     
  6. Nov 6, 2014 #5
    Thank you for the reply.
     
  7. Nov 6, 2014 #6

    Mark44

    Staff: Mentor

    It was the left side I was talking about, not the right side. Inside the brackets you should not have y'.
     
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