If `y(x-y)^2=x`, then `int1/(x-3y)dx` is equal to (A) `1/3log{(x-y)^2+1}` (B) `1/4log{(x-y)^2-1}` (C) `1/2log{(x-y)^2-1}` (D) `1/6 log{(x^2-y^2-1}`

If sin(x+y)=log(x+y) , then (dy)/(dx)= (a) 2 (b) -2 (c) 1 (d) -1

log (x + y) = log2 + (1) / (2) log x + (1) / (2) log y, then

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

Find y(x) , if it satisfies the following differential equation (dy)/(dx)=(x-y)^2 , and given that y(1)=1 (A) -ln|(1-x+y)/(1+x-y)|=2(x-1) (B) ln|(2-y)/(2-x)=x+y-1 (C) ln|(1-x+y)/(1+x-y)|=2(x-1) (D) 1/2ln|(1-x+y)/(1+x-y)|+ln|x|=0

Find y(x) , if it satisfies the following differential equation (dy)/(dx)=(x-y)^2 , and given that y(1)=1 (A) -ln|(1-x+y)/(1+x-y)|=2(x-1) (B) ln|(2-y)/(2-x)=x+y-1 (C) ln|(1-x+y)/(1+x-y)|=2(x-1) (D) 1/2ln|(1-x+y)/(1+x-y)|+ln|x|=0

If x^(y)=e^(x-y), then (dy)/(dx) is (1+x)/(1+log x)(b)(1-log x)/(1+log x)(c) not defined (d) (log x)/((1+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))

Statement I If y is a function of x such that y(x-y)^(2)= x, then int (dx)/(x-3y)=1/2 [ log (x-y)^(2)-1] Statement II int (dx)/(x-3y)=log (x-3y)+C

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)