Chapter 1.2, Problem 2E

To determine

(a)

To show:

The relation $y^2+x-3=0$ is an implicit solution to $dy/dx=-1/\left(2y\right)$ on the interval $\left(-\infty , 3\right)$.

To determine

(b)

To show:

The relation $x{y}^3-x{y}^{3}sinx=1$ is an implicit solution to $\frac{dy}{dx}=\frac{\left(xcosx+sinx-1\right)y}{3\left(x-xsinx\right)}$ on the interval $\left(0, \pi /2\right)$.