AP EAMCET · Maths · Differential Equations
If \(y=y(x)\) is the solution of the differential equation \(\left(\frac{2+\sin x}{y+1}\right) \frac{d y}{d x}+\cos x=0 \quad\) with \(y(0)=1\), then \(y\left(\frac{\pi}{2}\right)\) is equal to
- A \(\frac{1}{3}\)
- B \(\frac{2}{3}\)
- C 1
- D \(\frac{4}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
Given differential equation can be rewritten as \(\frac{d y}{1+y}+\frac{\cos x}{2+\sin x} d x=0\) Put \(2+\sin x=t \Rightarrow(\cos x) d x=d t\) \(\therefore \quad \frac{d y}{1+y}+\frac{1}{t} d t=0\) On integrating, we get…
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