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Separating variable DE to solve

  1. Sep 27, 2011 #1
    cos(x+y)dy=dx

    I have tried to solve it by
    Letting
    t = x+y

    But it's not going to be separated.. Some one plz help..
     
  2. jcsd
  3. Sep 27, 2011 #2
    Consider dx/dy. The equation becomes (1 +cost)=dt/dy.
     
  4. Sep 27, 2011 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    I don't see why you would say it does not become separable. If t= x+ y then dt= dx+ dy so dy= dt- dx. cos(x+y)dy= dx becomes cos(t)(dt- dx)= cos(t)dt- cos(t)dx= dx or cos(t)dt= (1+ cos(t))dx.
    [tex]dx= \frac{cos(t)}{1+ cos(t)}dt[/tex].
     
  5. Sep 27, 2011 #4
    I got the answer ..
    Let u=x+y
    du/dx=1+dy/dx
    dy/dx=du/dx-1
    Applying this:
    cos(x+y)dy=dx
    cos(x+y)dy/dx=1
    cosu(du/dx-1)=1
    du/dx-1=sec u
    du/dx=1+sec u
    dx/du=1/(1+sec u)
    x=integral of 1/(1+sec u) du
     
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