Find the equation of a curve if the slope is given by dy/dx=2y at point (1, 3) on the curve)

This problem requires integration; that is, find the function y = f(x) whose derivative is 2y, then plug in the coordinates of the given point (x, y) = 1, 3) to find the constant of integration c:

dy/dx = 2y

Integral of dy/dx with respect to x = Integral of 2y dx

y = 2xy + c

3 = 2(1)(3) + c

c = 3 - 6

c = -3

So, y = 2xy - 3

Answer:
y = 2xy - 3 <<<<< the equation of a curve whose slope is given by dy/dx=2y at point (1, 3) on the curve