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

The solution of the equation (dy)/(dx) +1/xtany =(1)/(x^(2))tan y sin y is:

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

Solve the differential equation: (i) (1+y^(2))+(x-e^( tan ^(-1)y))(dy)/(dx)=0 (ii) x(dy)/(dx)+cos^(2)y=tan y(dy)/(dx)

(dy) / (dx) tan y = sin (x + y) + sin (xy)

If tan ^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=a, prove that (dy)/(dx)=(x)/(y)((1-tan a))/((1+tan a))

(x (dy) / (dx) -y) tan ^ (- 1) ((y) / (x)) = x

(dy)/(dx)=y tan x , y=1 when x=0

If x="tan"(y)/(2)+"log tan"(y)/(2)-2log(1+"tan"(y)/(2)) , show that, (dy)/(dx)=(1)/(2)"sin"(1+sin y+cos y)