Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 240: 76

$y=x^{1/2}-2$ or, $y=\sqrt x-2$

The anti-derivative for $\dfrac{dy}{dx}=\dfrac{1}{2\sqrt x}$ is $y=x^{1/2}+C$ Apply the initial conditions $y(4)=0$. This implies $2+C=0 $ or, $C=-2$ Hence, $y=x^{1/2}-2$ or, $y=\sqrt x-2$