Question

x dy/dx=y(logy-logx+1)​

Answer 1

Answer:

x dy/dx=y(log y-log x+1)

x dy/dx=y log y-y logx +1

dy=y(logy−logx+1)

⇒dxdy=xy(logxy+1)

Put  y=vx⇒dxdy=v+xdxdv

⇒v+xdxdv=v(logv+1)

⇒vlogvdv=xdx

Integrating both sides,

⇒log(logv)=logx+logc=logcx

⇒logv=cx⇒logxy=cx