Question

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

• A. $ cos\text{ }x $
• B. $ \sec \text{ }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 } $