`(1-y)x(dy)/(dx)+(1+x)y=0`

Find the particular solution of y(1-x^2)(dy)/(dx)+x(1-y^2)=0 , given that y=0 when x=0

If y=sqrt((1-x)/(1+x)), find (dy)/(dx) and prove that (1-x^(2))(dy)/(dx)+y=0

lf y=sqrt((1-x)/(1+x)) find dy/dx and prove that (1-x^2)(dy)/(dx)+y=0

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

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

Find (dy)/(dx) if 1-x+y-x y=0

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 y=sin^(-1)x then prove that (1-x^(2))(d^(y))/(dx^(2))-x(dy)/(dx)=0