$$ \text { The degree of the differential equation } \sqrt{1+\left(\frac{d y}{d x}\right)^{1 / 3}}=\frac{d^2 y}{d x^2} \text { is: } $$

Let the population of a species of birds surviving at a time ' $\boldsymbol{t}$ ' be governed by the differential equation $\frac{d p}{d t}-p=-100$. If $p(0)=50$, then $p\left(-\log _e 2\right)$ is equal to

$$ \text { The particular solution of the differential equation }(x-y)(d x+d y)=(d x-d y) \text { when } y=-1 \text { and } x=0 \text { is } $$

The function $\boldsymbol{x}+\boldsymbol{y}=\boldsymbol{\operatorname { t a n }}^{-\mathbf{1}} \boldsymbol{y}$ is the solution of which of the following differential equations?