Equation of a Curve

Problem
Find the equation of the curve passing through the point (3, 2) and having s slope 5x2 - 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 (x2 + y2) / (y3 - 2xy)?
 

 
 
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