The solution of the differential equation dydx-y+3xloge(y+3x)+3=0 is: (where C is a constant of integration.)

dydx-y+3xln(y+3x)+3=0dy+3dx=(y+3x)ln(y+3x)dxln(y+3x)y+3x(d(y+3x))=dx  integrate both sidesln2(y+3x)2=x+c      let y+3x=t then the equation becomes ∫ln ttdt=lnt22 or x-12ln2(y+3x)=C