hi
The question in the attachment.
OK, this question will destroy my brain.
I want a start!
Because the original DE is homogeneous, use one of the two standard substitutions such as with Moreover, the following may prove useful:
and the same for even to the same power of 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.