derivates

v= yx dydx=xdvdx +vy=xv v= yx dydx=xdvdx +vy=xv 3.-(2x+3y+4)dx = (4x+6y+1)dy
v= yx dydx=xdvdx +v
y=xv
v= yx dydx=xdvdx +v
y=xv
dy dx=(2x+3y+4)(4x+6y+1) => dydx=(2+3yx+4)(4+6yx+1) =>
u=3v2+v-3 du=(6v+1)dv u=3v2+v-3 du=(6v+1)dv dy dx=(6+3v)(5+6v) => xdvdx +v=(6+3v)(5+6v) => x5+6vdvdx +6v2+5v=6+3v
u=3v2+v-3 du=(6v+1)dv
u=3v2+v-3 du=(6v+1)dv
x5+6vdvdx =-6v2-2v+6 => x5+6vdv=-6v2-2v+6vdx
5+6v-6v2-2v+6vdv=dxx => 5+6v3v2+v-3vdv=dxx => -125+6v3v2+v-3vdv=dxx
-125dv+6vdv3v2+v-3v=dxx => -125dv+6vdvu=dxx => --124dv+duu=dxx => -12u4dv=12duudxx => -4v23v2+v-3v-12Lnv=Lnx+Ln"c"
-4v2u-Lnv12=Lnxc => -4v2u=Lnv12+Lnxc => -4v2u=Lnxcv12
-2vu=Lnxcv12 => Ln2x+3y+2=2y-x+c