It's been quite a while since I last dealed with DE's. I'd appreciate if you could help me with the official, or usual, classification of the next DE's and/or if there are some definite methods to solve them. Hints will also be welcome:
$(1)\;\;\;\;\;\;\;\;y'=\frac{(y+2x-1)^2}{(4y+8x-6)(2y+4x-1)}\cdot\frac{1}{\sin\left(\frac{4y+8x-3}{y+2x-1}\right)}-2$
$(2)\;\;\;\;\;\;\;\;y'x+y\left(\ln^2x+\ln^2y-2\ln x\ln y\right)=0\;\;,\;x,y>0$
I'm guessing here one could write
$\ln^2x+\ln^2y-2\ln x\ln y=\left(\ln x-\ln y\right)^2=\ln^2\frac{x}{y}$
Thanks.