JEE Mains · Maths · STD 12 - 9. differential equations
If the solution \(y(x)\) of the given differential equation \(\left(e^y+1\right) \cos x d x+e^y \sin x d y=0\) passes through the point \(\left(\frac{\pi}{2}, 0\right)\), then the value of \(e^{y\left(\frac{\pi}{6}\right)}\) is equal to ...........
- A \(8\)
- B \(3\)
- C \(7\)
- D \(33\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\( \left(e^y+1\right) \cos x d x+e^y \sin x d y=0 \) \( \Rightarrow d\left(\left(e^y+1\right) \sin x\right)=0 \) \( \left(e^y+1\right) \sin x=C\) It passes through \(\left(\frac{\pi}{2}, 0\right)\) \(\Rightarrow \mathrm{c}=2\) Now, \(x=\frac{\pi}{6}\)…
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