If $x \log x \frac{d y}{d x}+y=\log x^2$ and $y(e)=0$, then $y\left(e^2\right)=$

If the order and degree of the differential equation $x \frac{d^2 y}{d x^2}=\left(1+\left(\frac{d^2 y}{d x^2}\right)^2\right)^{-1 / 2}$ are $k$ and $l$ respectively, then $k, l$ are the roots of

The equation of the curve passing through the point $(0, \pi)$ and satisfying the differential equation $y d x=\left(x+y^3 \cos y\right) d y$ is

The general solution of the differential equation $(x-(x+y) \log (x+y)) d x+x d y=0$ is