`(y+1)dy/dx+x(y^2+2y)=x`

If (dy)/dx = (xy)/(x^2 + y^2), y(1) = 1 and y(x) = e then x =

dy/dx =(y)/(2y^3+x)

Solve: (dy) / (dx) = (y (x + 2y)) / (x (2x + y)), y (1) = 2

(x + y (dy) / (dx)) / (yx (dy) / (dx)) = (x cos ^ (2) (x ^ (2) + y ^ (2))) / (y ^ ( 3))

Solve: x+y dy/dx=(a^2((x dy/dx-y))/(x^2+y^2))

The family of curves represented by (dy)/(dx)=(x^(2)+x+1)/(y^(2)+y+1) and the family represented by (dy)/(dx)+(y^(2)+y+1)/(x^(2)+x+1)=0

If x(dy)/(dx)=x^(2)+y-2, y(1)=1 , then y(2) equals ………………..