Differential Equations: (6x3y+2)dx(2xy1)dy=0

Help a stranger please. This is for my homework and I'm having a hard time solving these equations. Show the complete solutions and final answers please. It will be a great help. Thank you so much.

This covers Additional Topics on Equations of Order One, Coefficient Linear in Two Variables.

1. (6x-3y+2)dx-(2x-y-1)dy=0

2. (x+2y-1)dx-(2x+y-5)dy=0

Solution (1)
(6x3y+2)dx(2xy1)dy=0

Let
z=2xy

dy=2dxdz

(3z+2)dx(z1)(2dxdz)=0

(z+4)dx(z1)dz=0

dxz1z+4dz=0

dx(15z+4)dz=0

x[z5ln(z+4)]=c

x[(2xy)5ln(2xy+4)]=c

5ln(2xy+4)x+y=c
 

Please double check my solution. It is done in a hurry.

In reply to by Jhun Vert

Corrections
(6x3y+2)dx(2xy1)dy=0

Let
z=2xy

dy=2dxdz

(3z+2)dx(z1)(2dxdz)=0

(z+4)dx+(z1)dz=0

dx+z1z+4dz=0

dx+(15z+4)dz=0

x[z5ln(z+4)]=c

x+[(2xy)5ln(2xy+4)]=c

5ln(2xy+4)+3xy=c           answer