If `y=y(x)` and it follows the relation `4x e^(x y)=y+5sin^2x ,` then `y^(prime)(0)` is equal to______

If y=y(x) and it follows the relation e^(xy^2)+ycos(x^2)=5 then y'(0) is equal to

If y=y(x) and it follows the relation e^(xy^2)+ycos(x^2)=5 then y'(0) is equal to

If y = y(x) and it follows the relation e^(xy) + y cos x = 2 , then find (i) y'(0) and (ii) y"(0) .

If 2^x = cos(y/2) and a^x = sin y , then sin(y/2) is equal to

y=f(x) , where f satisfies the relation f(x+y)=2f(x)+x y(y)+ysqrt(f(x))AAx , y in Ra n df^(prime)(0)=0. Then f(6) is equal of f(-3) is ________

If y= y(x) ( 2 _ cos x ) /( y+1) (( dy )/(dx)) =- sin x, y (0) =1 then y((pi)/(2)) equal ____.

5.If y=e^x sin x ,then y_n is equal to

Area bounded by x ^(2) y ^(2)+ y ^(4)-x ^(2)-5y ^(2)+4=0 is equal to :

If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c x and y(0)=0 , then

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