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.