Chapter 11.3, Problem 49E

(a)

To determine

To prove: The equation $y^{″}=\frac{-y+x{y}^{\prime }}{y^2}$ if $y^{\prime }=-\frac{x}{y}$.

(b)

To determine

To prove: The equation $y^{″}=-\frac{\left(x^2+y^2\right)}{y^3}$ if $y^{\prime }=-\frac{x}{y}$.

(c)

To determine

The validity of statements $y^{″}=-\frac{4}{y^3}$ if $x^2+y^2=4$.