MHT CET · Maths · Differential Equations
If \(\mathrm{y}=\mathrm{y}(x)\) and \(\left(\frac{2+\sin x}{\mathrm{y}+1}\right) \frac{\mathrm{dy}}{\mathrm{d} x}=-\cos x\), \(y(0)=1\), then \(y\left(\frac{\pi}{2}\right)=\)
- A \(\frac{1}{3}\)
- B \(\frac{2}{3}\)
- C \(-\frac{1}{3}\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
\(\int \frac{\mathrm{dy}}{\mathrm{y}+1} = \int -\frac{\cos x}{2+\sin x} \mathrm{d}x\) \(\ln|\mathrm{y}+1| = -\ln|2+\sin x| + C\)
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