AP EAMCET · Maths · Differential Equations
If the general solution of the differential equation \(\cos ^2 x \frac{d y}{d x}+y=\tan x\) is \(y=\tan x-1+C e^{-\tan x}\) satisfies \(y\left(\frac{\pi}{4}\right)=1\), then \(C=\)
- A e
- B \(1\)
- C \(-1\)
- D \(\frac{1}{e}\)
Answer & Solution
Correct Answer
(A) e
Step-by-step Solution
Detailed explanation
Given, \(\cos ^2 x \frac{d y}{d x}+y=\tan x\) \(\Rightarrow \frac{d y}{d x}+y \sec ^2 x=\tan x \cdot \sec ^2 x\)...(i) Here, \(p=\sec ^2 x\) \(\Rightarrow \quad \int p d p=\int \sec ^2 x d x=\tan x\) \(I F=e^{\tan x}\) Multiplying Eq. (i) by \(I F\), we get…
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