DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

$\text{x}\frac{\text{dy}}{\text{dx}}+\cot\text{y}=0$

$\Rightarrow\text{x}\frac{\text{dy}}{\text{dx}}-\cot\text{y}$

$\Rightarrow\frac{1}{\text{x}}\ \text{dx}=-\frac{1}{\cot\text{y}}\ \text{dy}$

$\Rightarrow\frac{1}{\text{x}}\ \text{dx}=-\tan\text{y dy}$

Integrating both sides, we get

$\int\frac{1}{\text{x}}\ \text{dx}=-\int\tan\text{y dy}$

$\Rightarrow\int|\text{x}|=-\int|\sec\text{y}|+\int\text{C}$

$\Rightarrow\int|\text{x}|=-\int|\cos\text{y}|+\int\text{C}$

$\Rightarrow\text{x}=\text{C}\cos\text{y}$

Hence, $\text{x}=\text{C}\cos\text{y}$ is the required solution.