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

Solve the following differential equations. (i) (dy)/(dx) =(1+y^(2))/(1+x^(2)) (ii) (dy)/(dx) = (sqrt(1-y^(2)))/(sqrt(1-x^(2))) (iii) (dy)/(dx) = 2y tan hx (iv) sqrt(1+x^(2))dx + sqrt(1+y^(2))dy = 0 (v) (dy)/(dy) = e^(x-y)+x^(2)e^(-y)

If sqrt(x) + sqrt(y) = sqrt(a) , then (dy)/(dx) = 1/(2sqrt(x)) + 1/(2sqrt(y)) = 1/(2sqrt(a))

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

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

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

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

y=sqrt(x)+(1)/(sqrt(x)), prove that 2x(dy)/(dx)=sqrt(x)-(1)/(sqrt(x))

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

x sqrt(1+y)+y sqrt(1+x)=0 for, for,(dy)/(dx)=-(1)/((1+x)^(2))

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