Consider the equation

P(x,y)dx+Q(x,y)dy=0

a. Show that the equation has an integrating factor of the form (x,y)=f(xy)=f(z) if

[1/(yQxP)][P/yQ/x]

is a function of z=xy. Call this function h(z). Show that f is obtained from the equation

f/f=h

b. Show that the equation

ydx+[x+yx3(1+lny)]dy=0

is not exact. Use part (a) to find an integrating factor.

c. use the integrating factor from part (b) to transform the equation into an exact function. (show that the new equation is indeed exact)

d. find the general solution to the equation