Evaluate: (i) `|(x^2+x y+y^2,x+y ),(x^2-x y+y^2,x-y)|` (ii) `|(1,(log)_b a),((log)_a b,1)|`

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))

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

A: If y = x ^(y) then (dy)/(dx) = (y ^(2))/(x(1- log y )) If y = f (x) ^(y), then (dy)/(dx) = (y ^(2) f '(x))/(f (x) [1- ylog f (x)])= (y ^(2) f'(x))/(f (x) [1- log y])

The solution of ((dy)/(dx))^(2)+(2x+y)(dy)/(dx)+2xy=0, is (i) (y+x^(2)-c_(1))(x+log y+y^(2)+c_(2))( (ii) (y+x^(2)-c_(1))(x-log y-c_(2))( iii) (y+x^(2)-c_(1))(x+log y-c_(2))( iv) (y+x^(2)-c_(1))(3x+log y-c_(2))

For 0

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)}

The solution of (x^2+xy)dy=(x^2+y^2)dx is (A) logx=log(x-y)+y/x+C (B) logx=2log(x-y)+y/x+C (C) logx=log(x-y)+x/y+C (D) none of these

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