The solution of the differential equation dydx=x-2y+12x-4y is
x-2y2+2x=c
x-2y2+x=c
x-2y2+2x2=c
x-2y2+x2=c
Explanation for correct option
Given: dydx=x-2y+12x-y
Let x-2y=v
Differentiating with respect to x we get
⇒1-2dydx=dvdx⇒1-dvdx2=dydx
⇒1-dvdx2=v+12v⇒1-dvdx=v+1v⇒1-v+1v=dvdx⇒v-v-1v=dvdx⇒-1v=dvdx⇒-dx=vdv
integrating both sides
⇒-∫dx=∫vdv⇒-x=v22
putting v=x-2y
⇒-2x=x-2y2+C⇒x-2y2+2x=C
Hence, option A is correct.