`(1-x^2)(1-y)dx=x y(1+y)dy` y 4. (1 - x?) (1 - y) dx = xy (1 + y) dy

y(1-x^(2))dy=x(1+y^(2))dx

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

Solve dy/dx = xy + x + y + 1

If y = x/(x+a) ,show that x dy/dx = y (1- y)

Solve the following differential equations (i) (1+y^(2))dx = (tan^(-1)y - x)dy (ii) (x+2y^(3))(dy)/(dx) = y (x-(1)/(y))(dy)/(dx) + y^(2) = 0 (iv) (dy)/(dx)(x^(2)y^(3)+xy) = 1

(dy)/(dx)(1+x+y)=x+y+1

If y= (x)/( x+a) , prove that x (dy)/( dx) = y(1-y) .