If x ~d y=y( ~d x+y ~d y), y(1)=1, y(x)>0 , then y(-3) is

Step-by-step solution

x ~d y=y( ~d x+y ~d y) y ~d x= (x-y^2 ) d y d x ~d y + (- 1 y ) x=-y I.F. = e ^ - 1 d y y^y = e ^ - y = 1 y Solution of the given equation is x 1 y = -y 1 y ~d y+ c x y =-y+ c ....(i) Since y(1)=1 , i.e., y=1 when x=1 1=-1+c c=2 x y =-y+2 [ From (i) ] Putting x=-3 , we get - 3 y =-y+2 aligned & y^2-2 y-3=0 & (y-3)(y+1)=0 aligned Since y(x)>0, y=3