1)

The solution of the differential equation logxdydx+yx=sin2xis


A) ylog|x|=C1/2cosx

B) ylog|x|=C+1/2cos2x

C) ylog|x|=C1/2cos2x

D) xylog|x|=C1/2cos2x

Answer:

Option C

Explanation:

dydx+yxlogx=sin2xlogx

I.F. = edxxlogx

.'. I.F. = e1tdt = 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