The solution set of the system of equations `x+y=(2pi)/3,cosx+cosy=3/2,` where `xa n dy` are real, is ________

The solution of the differential equation dy/dx +y =cosx is -

The solution of the equation (dy)/(dx)=(3x-4y-2)/(3x-4y-3) is

The solution of the system of equations sin x sin y=(sqrt(3))/(4),cos x cos y=(sqrt(3))/(4) are x_(1)=(pi)/(3)+(pi)/(2)(2n+k);n,k in Iy_(1)=(pi)/(6)+(pi)/(2)(k-2n);n,k in Ix_(2)=(pi)/(6)+(pi)/(2)(2n+k);n,k in Iy_(2)=(pi)/(3)+(pi)/(2)(k-2n);n,k in I

The solution of the differential equation ((x+2y^(3))dy)/(dx)=y is

The solution of the equation (dy)/(dx) = (y^(2)-y-2)/(x^(2) +2x-3) is