The particular solution of the differential equation $$ \frac{d y}{d x}=\frac{x+y+1}{x+y-1} $$ when $$ \mathrm{x}=\frac{2}{3} $$ and $$ y=\frac{1}{3} $$ is

The order of the differential equation whose solution is $$y=a \cos x+b \sin x+c e^{-x}$$ is

The general solution of the differential equation $$(2 y-1) d x-(2 x+3) d y=0$$ is

The differential equation of the family of parabolas with focus at the origin and the $$X$$-axis a axis, is