1) The solution of the differential equation logxdydx+yx=sin2xis A) ylog|x|=C−1/2cosx B) ylog|x|=C+1/2cos2x C) ylog|x|=C−1/2cos2x D) xylog|x|=C−1/2cos2x Answer: Option CExplanation:dydx+yxlogx=sin2xlogx I.F. = e∫dxxlogx .'. I.F. = e∫1tdt = elogt = t = log |x| solution is given by y(I.F.) = ∫Q(I.F.)dx+C y log |x| = ∫sin2xlog|x|(log|x|)dx+C=−Cos2x2+C