# Equation of a Curve

**Problem**

Find the equation of the curve passing through the point (3, 2) and having s slope 5*x*^{2} - *x* + 1 at every point (*x*, *y*).

A. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{31}{3}$ | C. $y = 5x^3 - 2x^2 + x - 118$ |

B. $y = 5x^3 - 2x^2 + x - 31$ | D. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{83}{2}$ |

## 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} - 2xy)?