Chapter 5.2, Problem 43ES

Solve the initial-value problems.

(a) $\frac{dy}{dx}=\sqrt[3]{x},y\left(1\right)=2$

(b) $\frac{dy}{dt}=\sin t+1,y\left(\frac{\pi }{3}\right)=\frac{1}{2}$

(c) $\frac{dy}{dx}=\frac{x+1}{\sqrt{x}},y\left(1\right)=0$