## Equation of a curve with given equation of slope and passing through a point

**Problem**

What is the equation of the curve passing through the point (3, -2) and having a slope at any point (*x*, *y*) equal to (*x*^{2} + *y*^{2}) / (*y*^{3} - 2*xy*)?

**Problem**

What is the equation of the curve passing through the point (3, -2) and having a slope at any point (*x*, *y*) equal to (*x*^{2} + *y*^{2}) / (*y*^{3} - 2*xy*)?

**The Calculus**

Calculus is a branch of mathematics which uses derivative to analyze the way in which the values of a function vary. Developed on 17th century, Calculus has now applications almost in all areas of human endeavor: engineering, physics, business, economics, astronomy, chemistry, biology, psychology, sociology, etc. Sir Isaac Newton (1642 – 1727) and Gottfried Wilhelm Leibniz (1646 – 1716), working independently from each other, developed the Calculus in connections with their work. Newton used Calculus in finding the velocity of a moving body, the work done by force and the centroid of mass of a body. Leibniz on the other hand focused on geometric calculation like finding the tangent and normal to a curve, area bounded by two or more curves, and volume of a solid. Leibniz is the one who initiated the modern notation of *dx* and $\displaystyle \int$.

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The following are short descriptions of the circle shown below.

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