The solution of the differential equation $x\frac{dy}{dx}+y=x^3{y}^6$ , is 

detailed solution

Correct option is B

The given differential equation can be written as1y6dydx+1xy5=x2Let y−5=0 , Then −5y−6dydx=dvdx⇒y−6dydx=−15dvdxSubstituting these values in the given differential equation, we get−15dvdx+1xv=x2⇒ dvdx−5xv=−5x2          …(i)This is the standard form of the linear differential equation having integrating factor I. F. =e∫5xdx=e−5log⁡x=1x5Multiplying both sides of (i) by I.F. and integrating w.r.t. x, we get v1x5=∫−5x2⋅1x5dx⇒vx5=52x−2+C⇒ y−5x5=52x−2+C  , which is the required solution.