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Differential Equation-Separable Equations

  1. Sep 25, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the solution of the diff eq that satisfies the given initial coordinate

    2. Relevant equations
    xcosx=(2y + e^(3y)) y' , y(0)=0

    3. The attempt at a solution

    So I have the family of solutions:
    xsinx-cosx=y^2 + e^(3y)/3 + c

    and I know to put 0 in for the x's, but the solution is wrong, and it appears like I need to put 0 into the y's (yes I did say y's) but not sure why.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 25, 2010 #2


    Staff: Mentor

    Yes, substitute 0 for x and 0 for y. That's what y(0) = 0 means.

    You have a sign error in your solution. It should be xsinx + cosx = y^2 + e^(3y) + C.
  4. Sep 25, 2010 #3
    Thanks for the reply. And just to clarify, I have another problem where the initial condition is u(0)=-5 so I put in -5 for my x's and 0 for my y's?
  5. Sep 25, 2010 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If x is the dependent variable, that is, you have u(x), then you need to set x=0 and u=-5. You don't have x and y anymore, one of them has been replaced by a new function u in this other problem.
  6. Sep 25, 2010 #5
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