Chapter 4 - Section 4.8 - Antiderivatives - Exercises - Page 273: 96

$y=\sqrt x-2$

We need to find the anti-derivative for $\dfrac{dy}{dx}=\dfrac{1}{2\sqrt x}$ Thus, we have: $y=x^{1/2}+C$ Apply the initial condition $y(4)=0$ in the above equation to solve for $C$. we get: $2+C=0 \implies C=-2$ Hence, $y=x^{1/2}-2$ or, $y=\sqrt x-2$