If x d y=y d x+y^2 d y, y 0 and y(1)=1 , then what is y(-3) equal to?

Step-by-step solution

aligned & Given, x d y=y d x+y^2 d y & 1= y x d x d y + y^2 x & d x d y +y= x y aligned d x d y - x y =-y ...(1) aligned & P=- 1 y , Q=-y & IF =e^ P d y =e^ - 1 y d y =e^ - y = 1 y aligned Now, Solution of d.E. aligned & x ( I . F )= ( Q . I . F .) dy & x y = 1 y (-y) d y+C & x y = -1 d y+C & x y =-y+C & y(1)=1 aligned aligned & 1 1 =-1+C C=2 & x y =-y+2 x=-y^2+2 y & y(-3) -3=-y^2+2 y & y^2-2 y-3=0 & y= +2 4+12 2 = 2 4 2 & y=3,-1 & Since y 0 so y=3 aligned