`sin(xy) + (x)/(y) = x^(2) - y`

If sin(xy)+(y)/(x)=x^(2)-y^(2), find (dy)/(dx)

If x:y::5:2, then (x ^(2) - xy + y ^(2))/( x ^(2) + xy + y ^(2)) = ?

If y=e^(2 sin ^(-1)x) then |((x ^(2) -1) y ^('') +xy')/(y)| is equal to

If y=e^(2 sin ^(-1)x) then |((x ^(2) -1) y ^('') +xy')/(y)| is equal to

Solve x (dy) / (dx) sin ((y) / (x)) + xy sin ((y) / (x)) = 0 given y (1) = (pi) / (2)

If xe^(xy) + ye^(-xy) = sin ^(2) x , then (dy)/(dx) at x =0 is a) 2y^(2) -1 b) 2y c) y^(2) -y d) y^(2) -1

(sin x + sin y) / (sin x-sin y) = tan ((x + y) / (2)) * cot ((xy) / (2))

Verify that y= x sin x is a solution of differential equation xy' = y + x sqrt(x^(2) - y^(2) )

If x = sin alpha + sin beta, y = cos alpha + cos beta then tan alpha + tan beta = (1) (8xy) / (2 (y ^ 2-x ^ 2) + (x ^ 2 + y ^ 2 ) (x ^ 2 + y ^ 2-2)) (2) (4xy) / ((y ^ 2-x ^ 2) + (x ^ 2 + y ^ 2) (x ^ 2 + y ^ 2-2 )) (3) (8xy) / ((x ^ 2 + y ^ 2) (x ^ 2 + y ^ 2-2)) (4) 4xy