TS EAMCET · Maths · Differential Equations
If \(y=\sin x+A \cos x\) is the general solution of \(\frac{d y}{d x}+f(x) y=\sec x\), then an integrating factor of the differential equation is
- A \(\sec x\)
- B \(\tan x\)
- C \(\cos x\)
- D \(\sin x\)
Answer & Solution
Correct Answer
(A) \(\sec x\)
Step-by-step Solution
Detailed explanation
\(y=\sin x+A \cos x\)..(i) \(\frac{d y}{d x}=\cos x-A \sin x\)..(ii) From (i) and (ii), we get \(\cos x \frac{d y}{d x}+y \sin x=1 \Rightarrow \frac{d y}{d x}+\tan x \cdot y=\sec x\) \(\Rightarrow f(x)=\tan x ;\) I.F \(=e^{\int \tan x d x}=\mathrm{e}^{\ln |\sec x| d x}=\sec x\)
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