The differential equation of all straight lines passing through the point $(1, -1)$ is

The differential equation of the family of curves $r^2 = a^2 \cos 2\theta$,where '$a$' is an arbitrary constant,is:

If the order of a differential equation $\frac{d^2 y}{d x^2}-2\left(\frac{d y}{d x}\right)^3+\sin \left(\frac{d y}{d x}\right)+y=0$ is $l$ and the degree of the differential equation $\left(1+\frac{d^2 y}{d x^2}\right)^{\frac{2}{3}}=\left[2-\left(\frac{d y}{d x}\right)^3\right]^{\frac{3}{2}}$ is $m$, then the differential equation corresponding to the family of curves $y=A x^l+B e^{m x}$, where $A$ and $B$ are arbitrary constants, is

The differential equation of the family of straight lines whose slope is equal to $y$-intercept is

The differential equation whose solution is $(x - h)^2 + (y - k)^2 = a^2$ is ($a$ is a constant).

Form the differential equation of the family of lines $y = mx + \frac{4}{m}$ by eliminating the arbitrary constant $m$.