# Math Help - A proof concerning homogeneous DE's and integrating factors

1. ## A proof concerning homogeneous DE's and integrating factors

hi
The question in the attachment.
OK, this question will destroy my brain.
I want a start!

2. Because the original DE is homogeneous, use one of the two standard substitutions such as $y=ux,$ with $dy=x\,du+u\,dx.$ Moreover, the following may prove useful:

$M(x,y)=M(x,ux)=x^{n}M(1,u),$ and the same for $N,$ even to the same power of $x,$ because of the homogeneity of the DE. Then multiply through by your integrating factor, and see if you don't see some integrable combinations pop out at you.