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

1. Oct 8, 2011

### nousername

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. Oct 8, 2011

### ehild

Solve it as a quadratic equation for y.

ehild

3. Oct 8, 2011

### nousername

How do you do that? It has an x in it... Can you show me how? Thanks

4. Oct 8, 2011

### ehild

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

$3 y^2+(x^2)y-(5x+9)=0$

$y_1=\frac{-(x^2)+\sqrt{x^4+12(5x+9)}}{6}$

$y_2=\frac{-(x^2)-\sqrt{x^4+12(5x+9)}}{6}$

ehild

5. Oct 8, 2011

### jackmell

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:

$$x^5 y^4 + 3 y^3 x == 5 x^3 y^3 + 9$$

and that one too can be plotted nicely via ContourPlot

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