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

The solution of (dy)/(dx)=((x-1)^(2)+(y-2)^(2)tan^(-1)((y-2)/(x-1)))/((xy-2x-y+2)tan^(-1)((y-2)/(x-1))) is equal to

If f^(1)(x)=(1)/(1+(ln x)^(2)) and y=f(e^(tan x)) then (dy)/(dx) is equal to

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

y^(2)-(dy)/(dx)=x^(2)(dy)/(dx) A) y^(-1)+tan^(-1)x=c B) x^(-1)+tan^(-1)y=c C) y+tan^(-1)x=c D) x^(-1)+y^(-1)=tan^(-1)x+c

If e^(x)+e^(y)=e^(x+y), prove that (dy)/(dx)=-(e^(x)(e^(y)-1))/(e^(y)(e^(x)-1)) or,(dy)/(dx)+e^(y-x)=0

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

The solution of differential equation (1+x^(2)) (dy)/(dx) + y = e^(tan^(-1)x)

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

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