y=c log x-2

If x^(y)=y^(x) then (dy)/(dx)= ... (A) (y(x log y-y))/(x(y log x-x)) (B) (y(y log x-x))/(x(x log y-y)) (C) (y^(2)(1-log x))/(x^(2)(1-log y)) (D) (y(1-log x))/(x(1-log y))

If x^y = y^x , then dy/dx = ......... A) frac{y(x log y - y)}{x(y log x -x)} B) frac{y(y log x - x)}{x(x log y -y)} C) frac{y^2 (1- log x)}{x^2 (1- log y)} D) frac{y(1- log x)}{x(1-log y)}

If x ^( log y) = log x, then prove that (dy)/(dx) = (y)/(x) ((1- log x log y)/( (log x) ^(2)))

The solution of the differential equation log x (dy)/(dx) + (y)/(x) = sin 2x is a) y log | x | = C - (1)/(2) cos x b) y log |x| = C + (1)/(2) cos 2x c) y log | x| = C - (1)/(2) cos 2x d) xy log | x | = C - (1)/(2) cos 2x

The solution of the differential equation (dy)/(dx)=(x^(2)+xy+y^(2))/(x^(2)) is (A)tan^(-1)((x)/(y))^(2)=log y+c(B)tan^(-1)((y)/(x))=log x+c(C)tan^(-1)((x)/(y))=log x+c(D)tan^(-1)((y)/(x))=log y+c

The solution of the differential equation cos y log(sec x+tan x)dx=cos x log(sec y+tan y)dy is (a) sec^(2)x+sec^(2)y=c(b)sec x+sec y=c(c)sec x-sec y=c(d)Non of these

If x^(2) + y^(2)=6xy , prove that 2 log (x+ y)= log x + log y + 3 log 2

Assuming that all logarithmic terms are define which of the following statement(s) is/are incorrect? (A)log_b(ysqrtx)=log_b y.(1/2log_b x) , (B) log_b x-log_b y=(log_b x)/(log_b y) , (C)2(log_b x+log_b y)=log_b (x^2y^2) , (D) 4log_b x-log_b y=log(x^4/y^-3)