solve the differential equation- x2 dy/dx= 2xy+y2 Share with your friends Share 11 Vipin Verma answered this x2dydx = 2xy +y2So dydx = 2xy+y2x2=2yx+(yx)Let y =vx, so dydx = v +xdvdxSo dydx = v +xdvdx = 2v + v2Or xdvdx = v +v2Or dvv +v2 =dxxOr ∫dvv +v2=∫dxxOr ∫(1v-11+v)dv =∫dxxOr lnv -ln(1+v) = lnx + lnCOr lnv1+v = lnx +lnC ln(yx+y) = lnx +lnC = lnCxOr taking antilog,we getyx+y =Cx (ans) 27 View Full Answer
