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Can’t get a start on solving a first order differential equation

  1. May 25, 2012 #1
    1. The problem statement, all variables and given/known data
    Am looking at a first order, non linear differential equation. I want to solve for a general solution and will have to find a constant with given parameters. Equation: 3x2y+8xy2+[itex]([/itex]x3+8x2y+12y2[itex])[/itex][itex]dy/dx[/itex]=0 Parameters: y(2)=1


    2. Relevant equations
    [itex]∂M/∂y[/itex]=[itex]∂N/∂x[/itex] (Exactness) & [itex](My-Nx)/N[/itex] (integrating factors)

    3. The attempt at a solution
    I have tried to use separation of variable with no avail. When I try to separate them I can’t get it into terms of just x or just terms of y. I have tested for exactness and it failed, so I moved to the next step of integrating factors. After trying to solve for integrating factors I still cannot get function of x alone or y alone. When solveing for the equation listed in “Relevant equations” I get:((6xy+8y2-(24y+8x2))/(3x2y+8xy2).

    Have tried intergrating factors both ways and still can't get a function of x or y alone. Can someone point in the right direction to starting this problem. I am swinging the bat but missing the ball b/c I dont see it. Thank you
     
    Last edited by a moderator: May 25, 2012
  2. jcsd
  3. May 25, 2012 #2
    You must have computed [itex]M_{y}[/itex] and/or [itex]N_{x}[/itex] incorrectly, because they are equal.
     
    Last edited: May 25, 2012
  4. May 25, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    6xy+ 8y is My but 24y+ 8x2 is Ny, not Nx.

     
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