Find the equation of the curve?

Question

A curve passes through the point (0,8) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. what is the equation of the curve? (Use x as the independent variable)

Answer 1

y=8e^2x

Using Leibnitz notation:

dy/dx=2y

dy/y =2 dx

ln y =2x + c

ln 8 = c

ln y = 2x + ln 8

y = 8e^2x