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Graphing (x^2)y + 3y^2 = 5x + 9 or the like?

  1. Oct 8, 2011 #1
    1. The problem statement, all variables and given/known data

    Hey everyone. I have a mathematics exam coming up, and im always used to checking my answers using an alternative method. We have differentiation questions and i normally check them by graphing the equation on my calc and then graphing my calculated differential equation and see if the slope of the original function at any x-value (my calculator can calculate slopes) is the same as the y-value for my differential equation.

    My problem is, sometimes there are equations such as these: x2y + 3y2 = 5x + 9 which i cant graph because they have the y^2 and another y which isnt squared. My question is, does anybody know a way around this?

    2. Relevant equations

    x2y + 3y2 = 5x + 9

    3. The attempt at a solution

    I have no idea, i looked online but i didn't know what to google, so all the things that came up were just irrelevant.

    Any help would be appreciated.

    Thank you.
     
  2. jcsd
  3. Oct 8, 2011 #2

    ehild

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    Solve it as a quadratic equation for y.

    ehild
     
  4. Oct 8, 2011 #3
    How do you do that? It has an x in it... Can you show me how? Thanks
     
  5. Oct 8, 2011 #4

    ehild

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    The solution(s) of the quadratic equation will be functions of x.

    [itex]3 y^2+(x^2)y-(5x+9)=0[/itex]

    [itex]y_1=\frac{-(x^2)+\sqrt{x^4+12(5x+9)}}{6}[/itex]

    [itex]y_2=\frac{-(x^2)-\sqrt{x^4+12(5x+9)}}{6}[/itex]

    ehild
     
  6. Oct 8, 2011 #5


    Yeah, I gotta' way around this but you may not like my answer. It is however I feel the best approach to solving your dilemma: time to step into the 21st century and do away with that calculator and begin using Mathematica then just ContourPlot it:

    Code (Text):

    ContourPlot[x^2 y + 3 y^2 == 5 x + 9, {x, -15, 15}, {y, -15, 15}]
     
    Now I understand you need the algebra practice solving them manually but eventually you run into one you can't like:

    [tex] x^5 y^4 + 3 y^3 x == 5 x^3 y^3 + 9[/tex]


    and that one too can be plotted nicely via ContourPlot
     
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