## UnkleRhaukus 4 years ago $(3x-y+1)dx-(6x-2y-3)dy=0$

1. UnkleRhaukus

${dy \over dx}={3x-y+1 \over 6x-2y-3}$ 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)$

2. UnkleRhaukus

is this right?

3. Akshay_Budhkar

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

4. UnkleRhaukus

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

5. Akshay_Budhkar

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