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Homework Help: Please check my diffy q

  1. Apr 5, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the solution to each of the following initial value problems in explicit form.

    (a) y'=(2x)/(y+x2y), y(0)=-2

    2. Relevant equations

    Uhhhhh I suppose it would be relevant to mention that an equation in the form dy/dx = g(x)h(y) is separable

    3. The attempt at a solution

    y'=(2x)/(y+x2y)=[1/y][2x/(1+x2)]

    ==> y dy=2x/(1+x2) dx
    ==> y2/2 + C1 = ln|1+x2| + C2
    ==> y2/2 = ln|1+x2| + C (C = C2 - C1, just to combine into one constant)

    ==> (-2)2/2 = ln|1+02| + C
    ==> C = 2
    ==> y2 = 2ln|1+02| + 4
    ==> y = +/- √(2ln|1+x2| + 4)

    That just seems a little too complicated an answer. :yuck:
     
  2. jcsd
  3. Apr 5, 2010 #2
    I just don't understand the whole procedure. If I had put C on the left hand side of the equals sign, I would've came up with a different answer.
     
  4. Apr 5, 2010 #3
    How so? Leaving C on the left simply makes C=-2 as opposed to 2.
     
  5. Apr 5, 2010 #4
    which would change the initial value problem
     
  6. Apr 6, 2010 #5
    No it wouldn't -- not if C is on the left. Are you sure you aren't mixing C's? Had you left C on the left, then you wouldn't be using the equation above (in which C is on the right).
     
  7. Apr 6, 2010 #6
    Got'cha. Do you think the rest of the problem is right? I'm getting quite a few answers with "plus or minus" in this homework.
     
  8. Apr 6, 2010 #7
    Seems like you understand separable DEQs to me. It also doesn't hurt to check your answers by seeing if the answer satisfies the original DEQ.
     
  9. Apr 6, 2010 #8
    Horrible idea. Square roots and natural logs, combined, are a b***h to integrate.
     
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