Question

\[(3x-y+1)dx-(6x-2y-3)dy=0\]

Answer 1

\[{dy \over dx}={3x-y+1 \over 6x-2y-3}\]
let \[w= 6x-2y-3\]\[dw=6dx\]

\[dy={1 \over 2 }(w+5/w)6dw\]\[y=3 \int(1+5/w)dw\]\[y=3(w+5lnw)+c)\]

Answer 2

is this right?

Answer 3

u have taken
w=6x-2y-3
so if u differentiate shouldnt it be
dw=6dx - 2dy?

Answer 4

yeah that was the step that i was having problems with,
what am i supposed to do intergrate two regions?

Answer 5

lemme think i am not getting it.. did u try taking y= vx ? (y/x=v)