The number of solutions of $$\frac{d y}{d x}=\frac{y+1}{x-1}$$, when $$y(\mathrm{l})=2$$ is

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves $$c_1 y=\left(c_2+c_3\right) e^{x+c_4}$$ is

The general solution of the differential equation $$x^2 d y-2 x y d x=x^4 \cos x d x$$ is

The curve passing through the point $$(1,2)$$ given that the slope of the tangent at any point $$(x, y)$$ is $$\frac{3 x}{y}$$ represents