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

if y=x^(2)+(1)/(x^(2)+(1)/(x^(2)+............)) then prove that (dy)/(dx)=(2xy^(2))/(1+y^(2))

(dy)/(dx) = (2xy)/(x^(2)-1-2y)

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

(dy)/(dx)=(2xy)/(x^(2)-y^(2))

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

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

(1+x^(2))(dy)/(dx)+2xy=(1)/(1+x^(2));y=0 if x=1

The differential equations,find a particular solution satisfying the given condition: (1+x^(2))(dy)/(dx)+2xy=(1)/(1+x^(2));y=0 when x=1

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