$$ \text { The solution of } \boldsymbol{d} \boldsymbol{y}=\boldsymbol{\operatorname { c o s }} \boldsymbol{x}(\mathbf{2}-\boldsymbol{y} \boldsymbol{\operatorname { c o s e c }} \boldsymbol{x}) \boldsymbol{d} \boldsymbol{x} \quad \text { where } y=\sqrt{2} \text { when } x=\frac{\boldsymbol{\pi}}{4} \text { is } $$

The order and degree of the differential equation $\left(\frac{d y}{d x}\right)^2+\frac{d x}{d y}=x$ is:

In a bank the principal increases continuously at the rate of $4 \%$ per annum. In how many years will ₹ 1000 triple itself?

$$ \text { The particular solution of the equation } \sin \left(\frac{d y}{d x}\right)=a \text {, where } a \in \mathbb{R} \text { and } y=2 \text { when } x=0 \text { is } $$