Question

A curve passes through the point (0, 2) and has the property that
the slope of the curve at every point P is three times the y-coordinate
of P. Find an equation of the curve.

dy/dp = 3y
or ∫ (3/y) dy = ∫ dp
or 3 ln(y) = p + c
or @ (0,2)
ln(2) = 0 + c
or c = ln(2)
3 ln(y) = p + ln(2)
or y = e^( (p + ln(2)) ^(1/3) )

Answer 1

Odd notation. P is a point (x,y) so usually we would see

dy/dx = 3y

y = c*e^3x
2 = c, so

y = 2e^(3x)

You divided the right side by 3 and multiplied the left aside by 3, but that was not correct:

dy/dp = 3y
∫dy/y = ∫3dp
...