Chapter 2.6, Problem 31P

In each of Problem $25$ through $31$:

Find an integrating factor and solve the given equation.

Use a computer to draw several integral curves.

$\left(3x+\frac{6}{y}\right)+\left(\frac{x^2}{y}+3\frac{y}{x}\right)\frac{dy}{dx}=0$

Hint: See Problem $24$.

Show that if $(N_x-M_y)/(xM-yN)=R$, where $R$ depends on the quantity $xy$ only, then the differential equation $M+Ny\text{'}=0$ has integrating factor of the form $\mu (xy)$. Find a general formula for this integrating factor.