The differential equation, having general solution as $A x^2+B y^2=1$, where $A$ and $B$ are arbitrary constants, is

A radio active substance has half-life of $h$ days, then its initial decay rate is given by Note that at $\mathrm{t}=0, \mathrm{M}=\mathrm{m}_{\mathrm{o}}$

The differential equation of $y=\mathrm{e}^x\left(\mathrm{a}+\mathrm{bx}+x^2\right)$ is

An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half of the quantity of ice melts in 15 minutes. $x_0$ is the initial quantity of ice. If after 30 minutes the amount of ice left is $\mathrm{kx}_0$, then the value of $k$ is