`log_e(x+y)=2x y` then `y'(0)` is

If y=x^3(log)_e(1+x) , then y'(0) is equal to.......

If log_(e) (x^(4) y) = a and log_(e) (x^(2) y^(2)) = b, then log_(e) sqrt(y) in terms of a and b is

Let y=y(x) be the solution of the differential equation,x((dy)/(dx))+y=x log_(e)x,(x>1) if 2y(2)=log_(e)4-1, then y(e) is equal to: (a)-((e)/(2))(b)-((e^(2))/(2))(c)(e)/(4)(d)(e^(2))/(4)

IF y = y (x) is the solution of the differential equation, x (dy)/(dx) = y (log_(e) y - log_(e) x + 1) , when y(1) = 2, then y(2) is equal to _______

If log(x-y)-log5-(1)/(2)log x-(1)/(2)log y=0 then (x)/(y)+(y)/(x) is equal to

If ln(ln x-ln y)=e^(x^(2)y)(1-ln x) , then y'(e) equals

The solution of the differential equation, dy/dx=(x-y)^(2) , when y(1)=1, is (A) log_(e) abs((2-y)/(2-x))=2(y-1) (B) -log_(e)abs((1+x-y)/(1-x+y))=x+y-2 (C) log_(e) abs((2-x)/(2-y))=x-y (D) -log_(e) abs((1-x+y)/(1+x-y))=2(x-1)

y=log_e((1+x^2)/(1-x^2)) then find 225(y''-y') at x=1/2