The curve `y=(cosx+y)^(1/2)` satisfies the differential equation :

Verify that the function x+y = tan^(-1)y satisfies the differential equation y^(2)y' + y^(2) +1=0

Verify that the function x+y = tan^(-1)y satisfies the differential equation y^(2)y' + y^(2) +1=0

If the curve y=f(x) passing through the point (1,2) and satisfies the differential equation xdy+(y+x^(3)y^(2))dx=0 ,then

The curve that satisfies the differential equation y'=(x^(2) + y^2)/(2xy) and passes through (2,1) is a hyperbola with eccentricity :

A curve passes through (1,0) and satisfies the differential equation (2x cos y+3x^(2)y)dx+(x^(3)-x^(2)sin y-y)dy=0

Verify that y=A\ cos x+sinx satisfies the differential equation cosx \ (dy)/(dx)+(sinx) \ y=1.

find the equation of the curve which passes through the point (2,2) and satisfies the differential equation y-x(dy)/(dx)=y^(2)+(dy)/(dx)

The equation of curve through point (1,0) which satisfies the differential equation (1+y^(2))dx- xy dy = 0 , is

If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation, y(1+x y)dx""=x""dy , then f(-1/2) is equal to: