Marco

The equation looked something like this…

(1)\begin{align} \definecolor{blue}{rgb}{.525,.631,.922}\pagecolor{blue} xy + (x^2 - ye^y)y' = 0 \end{align}

(2)
\begin{align} \definecolor{blue}{rgb}{.525,.631,.922}\pagecolor{blue} M + Ny'=0 \end{align}

The book only mentioned this equation:

(3)\begin{align} \definecolor{blue}{rgb}{.525,.631,.922}\pagecolor{blue} \frac{d\mu}{dx}=\frac{M_y - N_x}{N}\mu \end{align}

The other equation is simply the following:

(4)\begin{align} \definecolor{blue}{rgb}{.525,.631,.922}\pagecolor{blue} \frac{d\mu}{dy}=\frac{N_x - M_y}{M}\mu \end{align}

Using this equation, it is easily seen that:

(5)\begin{align} \definecolor{blue}{rgb}{.525,.631,.922}\pagecolor{blue} \frac{d\mu}{dy}=\frac{2x - x}{xy}\mu=\frac{\mu}{y} \end{align}

Solving the equation like in the book example yields:

(6)\begin{align} \definecolor{blue}{rgb}{.525,.631,.922}\pagecolor{blue} \mu=y \end{align}