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Differential equation parametrisation with integrating factor

  1. Feb 12, 2013 #1
    1. The problem statement, all variables and given/known data

    Use parametrisation first, derive the equation including y and p = [itex]\frac{dy}{dx}[/itex] and use the integrating factor method to reduce it to an exact equation. Leave the solution in implicit parametric form.

    [itex](y')^{3}[/itex] + y[itex]^{2}[/itex] = xyy'


    3. The attempt at a solution

    I'm really lost at this. I tried writing p=y'
    p[itex]^{3}[/itex] + y[itex]^{2}[/itex]=xyp
    [itex]\frac{p^{3}+y^{2}}{yp}[/itex] = x
    [itex]\frac{p^{3}}{yp}[/itex] + [itex]\frac{y^{2}}{yp}[/itex] = x
    [itex]\frac{p^{2}}{y}[/itex] + [itex]\frac{y}{p}[/itex] = x

    And I don't really know what to do from there. Some facebook rumors propose that the integrating factor be [itex]\frac{1}{y^{3}}[/itex]
     
  2. jcsd
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