Question

The integrating factor of linear differential equation $\frac{dy}{dx}+y\tan x-\sec x=0$

• A. $cosx$
• B. $\sec x$
• C. $e^{\cos x}$
• D. $e^{\sin x}$

Answer 1

Answer: (B)

Let $x_1,x_2,...x_n$ be n observations. Then, $\overline{X}=\frac{1}{n}\Sigma y_i$ Let $y_i=\frac{x_i}{\alpha }+10$ (according to the given condition) Then, $\overline{Y}=\frac{1}{n}\Sigma y_i$ $=\frac{1}{n}\Sigma \left(\frac{x_i}{\alpha }+10\right)$ $=\frac{1}{\alpha }\left(\frac{1}{n}\Sigma x_i\right)+\frac{1}{n}(10n)$ $=\frac{1}{\alpha }\overline{X}+10$ $\Rightarrow$ $\overline{Y}=\frac{\overline{X}+10\alpha }{\alpha }$