Chapter 4 - Section 4.8 - Antiderivatives - Exercises - Page 273: 95

$y=9x^{1/3}+4$

We need to find the anti-derivative for $\dfrac{dy}{dx}=3x^{-2/3}$ Thus, we have $y=9x^{1/3}+C$ Apply the initial condition $y(-1)=-5$ in the above equation to solve for $C$. we get: $-9+C=-5 \implies C=4$ Hence, $y=9x^{1/3}+4$