`(x^(2)+y ^(2)) dy = xydx. If y (x _(o)) =e, y (1)=1,` then the value of `x _(o)` is equal to :

If y=e^(1+log_(e)x) , then the value of (dy)/(dx) is equal to

If e^(x)=y+sqrt(1+y^(2) then the value of y is

If y = x^(1/x) , the value of (dy)/(dx) at x =e is equal to

Let y(x) is the solution of the differential equation (x+2)(dy)/(dx)-(x+1)y=2 . If y(0)=-1 , then the value of y(2) is equal to

if y^x-x^y=1 then the value of (dy)/(dx) at x=1 is

If (x^2+y^2)dy=xydx and y(1)=1 and y(x_o)=e , then x_o=

if ( dy )/(dx) =1 + x +y +xy and y ( -1) =0 , then the value of ( y (0) +3 - e^(1//2))

Let y=f (x) and x/y (dy)/(dx) =(3x ^(2)-y)/(2y-x^(2)),f(1)=1 then the possible value of 1/3 f(3) equals :

Let y=f(x) satisfies (dy)/(dx)=(x+y)/(x) and f(e)=e then the value of f(1) is

If the solution of the differential equation (1+e^((x)/(y)))dx+e^((x)/(y))(1-(x)/(y))dy=0 is x+kye^((x)/(y))=C (where, C is an arbitrary constant), then the value of k is equal to