If `x ( 1+ y) ^ (1/2) + y ( 1+ x ) ^( 1/2) =0 ` then dy / dx is

If x sqrt ( 1+ y) + y sqrt( 1+x) =0 , prove that (dy)/( dx) = - (1)/( (1+x)^2) .

If (dy)/dx = (xy)/(x^2 + y^2), y(1) = 1 and y(x) = e then x =

if ( dy )/(dx) =1 + x +y +xy and y ( -1) =0 , then the value of ( y (0) +3 - e^(1//2))

If x dy =y (dx+y dy), y(1) =1 and Y(x)gt 0 . Then, y (-3) is epual to

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

Solve the differential equation: (i) (1+y^2) + ( x - e^(tan^-1 y) ) dy/dx = 0 (ii) x dy/dx + cos^2 y = tan y dy/dx

Solve x(y^2-1)dx - y(x^2-1)dy =0

If x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2) , prove that dy/dx+x/y=0

dy/dx + sqrt(((1-y^2)/(1-x^2))) = 0

if y = tan^-1(2^x/(1+2^(2x+1))) then dy/dx at x =0 is