A curve is such that dy/dx=2-8(3x+4)^-0.5

Question

The curve intersects the y-axis where y=4/3
Find the equation of the cure.

Answer 1

dy/dx=2-8(3x+4)^-0.5
y = 2x + (16/9)(3x + 4)^(-3/2) + c
or
y = 2x + (16/9)(1/√(3x+4)^(3/2) + c

but (0, 4/3) lies on it , so

4/3 = 2(0) + (16/9)(1/4^(3/2) + c
4/3 = (16/9)(1/8) + c
c = 6

y = 2x + (16/9)(3x + 4)^(-3/2) + 6

check my algebra, should have written it out on paper first.