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Solve ODE using method of integrating factors.

  1. Dec 14, 2006 #1
    1. The problem statement, all variables and given/known data
    solve the following equation using method of intergrating factors:


    2. Relevant equations
    dy/dx = y + cosx - sinx


    3. The attempt at a solution

    i think i have to get it in the form dy/dx + r(x)y = f(x)

    but i can't see how,

    if i multiply or divide by a factor i wont have dy/dx on its own. and how do i identify whats f(x) and r(x)?

    i also tried

    dy + (-y -cosx +sinx)dx = 0

    and then just finding a factor to make it an exact differntial, but im not sure how i determine the factor.
     
  2. jcsd
  3. Dec 14, 2006 #2
    simply subtract the y from both sides...
    dy/dx -y = cosx - sinx

    your function in front of y is simply a constant function (-1)
     
  4. Dec 14, 2006 #3
    its kinda obvious that y=sin(x) is a solution....
     
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