(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A curve passing through (3,-2) has a slope given by (x^2 + y^2)/(y^3 - 2xy). Find the equation of the curve.

2. Relevant equations

3. The attempt at a solution

My first thought was to plug in the points (3,-2) into the slope equation and plug them into the line equation (y - y1) = m(x - x1). Is that wrong? Seemed too easy for it to be a problem for differential equations..

So, I found that i could make the slope equation into an exact equation and solved for it.

I found that the answer i get is:

with c = -17

f(x,y) = x^3/3 + xy^2 - y^4/4 - 17

However that is not the equation of the curve. Is that the equation of the tangent line at (3,-2)?

I am stuck at this point, I am pretty sure I am done with 90% of the work, but I can't seem to figure out the equation of the curve from here on.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Differential Equations - Find equation of line

**Physics Forums | Science Articles, Homework Help, Discussion**