If $a$ and $b$ are the arbitrary constants, then the differential equation corresponding to the family of curves given by $y=x[a \cos (\log x)+b \sin (\log x)]$ is

If the solution for the differential equation $y^2 d x+\left(x^2-x y-y^2\right) d y=0$ at $(2,1)$ is $x+y=k\left(x y^2-y^3\right)$, then $k=$

The general solution of the differential equation $\frac{d y}{d x}+\frac{y}{x}=x^2$ is

If the order and degree of the differential equation corresponding to the family of curves $y^2=4 a(x+a)(a$ is parameter) are $m$ and $n$ respectively, then $m+n^2=$