JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be solution of the following differential equation \(e^{y} \frac{d y}{d x}-2 e^{y} \sin x+\sin x \cos ^{2} x=0, y\) \(\left(\frac{\pi}{2}\right)=0\). If \(y(0)=\log _{e}\left(\alpha+\beta e^{-2}\right)\), then \(4(\alpha+\beta)\) is equal to \(....\)
- A \(2\)
- B \(5\)
- C \(4\)
- D \(3\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\(\text { Let } e^{y}=t\) \(\Rightarrow \frac{d t}{d x}-(2 \sin x) t=-\sin x \cos ^{2} x\) \(\text { I.F. }=e^{2 \cos x}\) \(\Rightarrow t=e^{2 \cos x}=\int e^{2 \cos x}\left(-\sin x \cos ^{2} x\right) d x\)…
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