MHT CET · Maths · Differential Equations
The general solution of the differential equation. \(\frac{\mathrm{dy}}{\mathrm{d} x}+\sin \left(\frac{x+\mathrm{y}}{2}\right)=\sin \left(\frac{x-\mathrm{y}}{2}\right)\) is
- A \(\log \tan \left(\frac{y}{2}\right)=c-2 \sin \frac{x}{2}\), where \(c\) is the constant of integration
- B \(\log \tan \left(\frac{\mathrm{y}}{4}\right)=\mathrm{c}-2 \sin \left(\frac{x}{2}\right)\), where c is the constant of integration
- C \(\log \left[\tan \left(\frac{\mathrm{y}}{2}+\frac{\pi}{4}\right)\right]=\mathrm{c}-2 \sin x\), where c is the constant of integration
- D \(\log \left[\tan \left(\frac{\mathrm{y}}{4}+\frac{\pi}{4}\right)\right]=\mathrm{c}-2 \sin \frac{x}{2}\), where c is the constant of integration
Answer & Solution
Correct Answer
(B) \(\log \tan \left(\frac{\mathrm{y}}{4}\right)=\mathrm{c}-2 \sin \left(\frac{x}{2}\right)\), where c is the constant of integration
Step-by-step Solution
Detailed explanation
\(\frac{\mathrm{dy}}{\mathrm{d} x} = \sin \left(\frac{x-\mathrm{y}}{2}\right) - \sin \left(\frac{x+\mathrm{y}}{2}\right)\) \(\frac{\mathrm{dy}}{\mathrm{d} x} = 2 \cos\left(\frac{x}{2}\right) \sin\left(-\frac{y}{2}\right)\)
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